CN111488552B - Close-proximity multi-target tracking method based on Gaussian mixture probability hypothesis density - Google Patents

Close-proximity multi-target tracking method based on Gaussian mixture probability hypothesis density Download PDF

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CN111488552B
CN111488552B CN202010332381.9A CN202010332381A CN111488552B CN 111488552 B CN111488552 B CN 111488552B CN 202010332381 A CN202010332381 A CN 202010332381A CN 111488552 B CN111488552 B CN 111488552B
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张欢庆
刘杰
贾廷见
刘黎明
丁伟
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Abstract

本发明公开了一种基于高斯混合概率假设密度的紧邻多目标跟踪方法，包括如下步骤：增加标签和历史状态矩阵为辅助参数构建目标的新标准描述集；初始化目标概率假设密度、目标标签集及目标历史状态矩阵集；根据新生目标和存活目标的概率假设密度、标签集、历史状态矩阵集计算目标预测概率假设密度、目标预测标签集、目标预测历史状态矩阵集；基于量测集计算目标后验概率假设密度、目标后验标签集和目标后验历史状态矩阵集，重分配目标后验概率假设密度中各高斯分量的权值；变换目标的高斯分量集及参数集，约简变换后的高斯分量集；估计目标的状态和数目；若跟踪单一时刻则跟踪结束；若跟踪若干时刻则迭代所有时刻。本发明有良好的跟踪性能和鲁棒性。

Figure 202010332381

The invention discloses a method for tracking multiple targets in close proximity based on Gaussian mixture probability hypothesis density, comprising the following steps: adding labels and historical state matrices as auxiliary parameters to construct a new standard description set for the target; initializing the target probability hypothesis density, target label set and Target historical state matrix set; Calculate the target prediction probability hypothesis density, target prediction label set, target prediction historical state matrix set based on the probability hypothesis density, label set, and historical state matrix set of newborn targets and surviving targets; calculate the target based on the measurement set The posterior probability hypothesis density, the target posterior label set and the target posterior historical state matrix set, redistribute the weight of each Gaussian component in the target posterior probability hypothesis density; transform the Gaussian component set and parameter set of the target, and reduce the transformed Gaussian component set; estimate the state and number of targets; if tracking a single moment, the tracking ends; if tracking several moments, iterate over all moments. The invention has good tracking performance and robustness.

Figure 202010332381

Description

基于高斯混合概率假设密度的紧邻多目标跟踪方法Proximity Multiple Target Tracking Method Based on Gaussian Mixture Probability Hypothesis Density

技术领域technical field

本发明属于智能信息处理技术领域，具体涉及一种基于高斯混合概率假设密度的紧邻多目标跟踪方法。The invention belongs to the technical field of intelligent information processing, and in particular relates to a method for tracking multiple targets in close proximity based on Gaussian mixture probability hypothesis density.

背景技术Background technique

近年来，基于有限集统计理论的概率假设密度(Probability hypothesisdensity,PHD)滤波器因无需复杂的数据关联过程，极大地降低了计算复杂度，引起了多目标跟踪领域学者的广泛关注。In recent years, the Probability hypothesis density (PHD) filter based on finite set statistics theory has greatly reduced the computational complexity because it does not require complex data association process, which has attracted extensive attention from scholars in the field of multi-target tracking.

PHD滤波器是多目标贝叶斯滤波器的一种近似方法，它在每一时刻传递的并不是目标的完全后验密度，而是目标的概率假设密度(目标完全后验密度的一阶统计矩)，目标状态及数目从该目标概率假设密度中获取。然而，PHD滤波器迭代过程无法直接求得闭合解。线性高斯动态系统中，PHD滤波器的闭合解可以采用高斯混合方式来实现，即利用多个高斯分量的加权和来近似目标概率假设密度，这种方法称为GM-PHD滤波器。该滤波器的递推过程如下：The PHD filter is an approximation method of the multi-objective Bayesian filter. What it transmits at each moment is not the complete posterior density of the target, but the probability hypothesis density of the target (the first-order statistics of the complete posterior density of the target moment), the target state and number are obtained from the target probability hypothesis density. However, the iterative process of the PHD filter cannot directly obtain the closed solution. In a linear Gaussian dynamic system, the closed solution of the PHD filter can be realized by Gaussian mixture, that is, the weighted sum of multiple Gaussian components is used to approximate the target probability hypothesis density. This method is called GM-PHD filter. The recursive process of the filter is as follows:

预测步：k-1时刻，假设目标概率假设密度

Figure BDA0002465416630000011
可由高斯混合表示为：Prediction step: k-1 time, assume the target probability hypothesis density
Figure BDA0002465416630000011
It can be represented by a Gaussian mixture as:

Figure BDA0002465416630000012
Figure BDA0002465416630000012

式中，

Figure BDA0002465416630000013
表示一个均值为m，协方差为P的高斯密度，x表示高斯分量o的状态，o为表示目标的高斯分量，其标准描述集为o＝{w,m,P}，
Figure BDA0002465416630000014
和
Figure BDA0002465416630000015
分别表示第i个高斯分量的权值、均值和协方差矩阵，Jk-1表示高斯分量的数目；In the formula,
Figure BDA0002465416630000013
Represents a Gaussian density with mean m and covariance P, x represents the state of Gaussian component o, o is the Gaussian component representing the target, and its standard description set is o={w,m,P},
Figure BDA0002465416630000014
and
Figure BDA0002465416630000015
Represent the weight, mean and covariance matrix of the i-th Gaussian component respectively, and J k-1 represents the number of Gaussian components;

k时刻，目标预测概率假设密度

Figure BDA0002465416630000016
的表达式为：At time k, the target prediction probability hypothesis density
Figure BDA0002465416630000016
The expression is:

Figure BDA0002465416630000017
Figure BDA0002465416630000017

式中，

Figure BDA0002465416630000018
表示k时刻第i个存活高斯分量
Figure BDA0002465416630000019
的预测权值，
Figure BDA00024654166300000110
表示k时刻第i个存活高斯分量
Figure BDA00024654166300000111
的预测均值，
Figure BDA00024654166300000112
表示k时刻第i个存活高斯分量
Figure BDA00024654166300000113
的预测协方差矩阵，
Figure BDA00024654166300000114
表示k时刻第j个新生高斯分量
Figure BDA00024654166300000115
的权值，
Figure BDA00024654166300000116
表示k时刻第j个新生高斯分量
Figure BDA00024654166300000117
的均值，
Figure BDA00024654166300000118
表示k时刻第j个新生高斯分量
Figure BDA00024654166300000119
的协方差矩阵，Js,k|k-1表示存活高斯分量的预测数目，Jγ,k表示新生高斯分量的数目。In the formula,
Figure BDA0002465416630000018
Indicates the i-th surviving Gaussian component at time k
Figure BDA0002465416630000019
the predictive weight of
Figure BDA00024654166300000110
Indicates the i-th surviving Gaussian component at time k
Figure BDA00024654166300000111
the predicted mean of
Figure BDA00024654166300000112
Indicates the i-th surviving Gaussian component at time k
Figure BDA00024654166300000113
The prediction covariance matrix of ,
Figure BDA00024654166300000114
Indicates the jth newborn Gaussian component at time k
Figure BDA00024654166300000115
the weight of
Figure BDA00024654166300000116
Indicates the jth newborn Gaussian component at time k
Figure BDA00024654166300000117
the mean value of
Figure BDA00024654166300000118
Indicates the jth newborn Gaussian component at time k
Figure BDA00024654166300000119
The covariance matrix of , J s,k|k-1 represents the predicted number of surviving Gaussian components, and J γ,k represents the number of newborn Gaussian components.

更新步：利用k时刻量测集Zk更新目标预测概率假设密度

Figure BDA0002465416630000021
则目标后验概率假设密度
Figure BDA0002465416630000022
可表示为：Update step: Utilize the measurement set Z k at time k to update the target prediction probability hypothesis density
Figure BDA0002465416630000021
Then the target posterior probability hypothesis density
Figure BDA0002465416630000022
Can be expressed as:

Figure BDA0002465416630000023
Figure BDA0002465416630000023

式中，pd表示检测概率，

Figure BDA0002465416630000024
表示基于量测集Zk中任一量测z更新后的目标后验概率假设密度；In the formula, p d represents the detection probability,
Figure BDA0002465416630000024
Represents the target posterior probability hypothesis density updated based on any measurement z in the measurement set Z k ;

Figure BDA0002465416630000025
Figure BDA0002465416630000025

式中，Jk|k-1表示用k时刻高斯分量的预测数目，

Figure BDA0002465416630000026
表示基于量测z的第i个高斯分量
Figure BDA0002465416630000027
的权值，
Figure BDA0002465416630000028
表示基于量测z的第i个高斯分量
Figure BDA0002465416630000029
的均值，
Figure BDA00024654166300000210
表示第i个高斯分量
Figure BDA00024654166300000211
的协方差矩阵；In the formula, J k|k-1 represents the predicted number of Gaussian components at time k,
Figure BDA0002465416630000026
Represents the ith Gaussian component based on the measurement z
Figure BDA0002465416630000027
the weight of
Figure BDA0002465416630000028
Represents the ith Gaussian component based on the measurement z
Figure BDA0002465416630000029
the mean value of
Figure BDA00024654166300000210
Represents the i-th Gaussian component
Figure BDA00024654166300000211
The covariance matrix of ;

Figure BDA00024654166300000212
Figure BDA00024654166300000212

式中，

Figure BDA00024654166300000213
表示杂波强度，
Figure BDA00024654166300000214
表示用k-1时刻第i个高斯分量
Figure BDA00024654166300000215
的权值
Figure BDA00024654166300000216
所预测的k时刻高斯分量
Figure BDA00024654166300000217
的预测权值；
Figure BDA00024654166300000218
表示用k-1时刻第i个高斯分量
Figure BDA00024654166300000219
的均值
Figure BDA00024654166300000220
所预测的k时刻高斯分量
Figure BDA00024654166300000221
的预测均值；
Figure BDA00024654166300000222
表示用k-1时刻第i个高斯分量
Figure BDA00024654166300000223
的协方差矩阵
Figure BDA00024654166300000224
所预测的k时刻高斯分量
Figure BDA00024654166300000225
的预测协方差矩阵；Hk表示k时刻量测矩阵；Rk表示k时刻量测噪声协方差矩阵，
Figure BDA00024654166300000226
表示第l个预测高斯分量
Figure BDA00024654166300000227
的预测权值，
Figure BDA00024654166300000228
表示第l个预测高斯分量
Figure BDA00024654166300000229
的预测均值，
Figure BDA00024654166300000230
表示第l个预测高斯分量
Figure BDA00024654166300000231
的预测协方差矩阵。In the formula,
Figure BDA00024654166300000213
Indicates the clutter intensity,
Figure BDA00024654166300000214
Represents the i-th Gaussian component at time k-1
Figure BDA00024654166300000215
weight of
Figure BDA00024654166300000216
The predicted Gaussian component at time k
Figure BDA00024654166300000217
the predictive weight of
Figure BDA00024654166300000218
Represents the i-th Gaussian component at time k-1
Figure BDA00024654166300000219
mean of
Figure BDA00024654166300000220
The predicted Gaussian component at time k
Figure BDA00024654166300000221
The predicted mean value of ;
Figure BDA00024654166300000222
Represents the i-th Gaussian component at time k-1
Figure BDA00024654166300000223
The covariance matrix of
Figure BDA00024654166300000224
The predicted Gaussian component at time k
Figure BDA00024654166300000225
The prediction covariance matrix of ; H k represents the measurement matrix at time k; R k represents the measurement noise covariance matrix at time k,
Figure BDA00024654166300000226
Indicates the lth predicted Gaussian component
Figure BDA00024654166300000227
the predictive weight of
Figure BDA00024654166300000228
Indicates the lth predicted Gaussian component
Figure BDA00024654166300000229
the predicted mean of
Figure BDA00024654166300000230
Indicates the lth predicted Gaussian component
Figure BDA00024654166300000231
The prediction covariance matrix of .

目前，基于高斯混合(Gaussian mixture，GM)近似方式的概率假设密度滤波方法已经在实际应用中得到验证。杂波跟踪环境下，GM-PHD滤波器因具有较高迭代效率及状态提取方便等优势，被广泛用于线性高斯动态模型的目标跟踪系统。然而，基于PHD滤波的多目标跟踪方法是假设跟踪场景中目标之间的距离较远，即目标间不存在相互干扰；但真实跟踪环境下，多个目标为了实现相互协同工作，这些目标间的距离通常可能非常小，即紧邻目标(交叉运动的目标和平行运动的目标)。当跟踪场景中的多个目标相互接近或保持近距离运动状态时，基于PHD滤波的多目标跟踪方法便不能正确地区分出源于每个目标自身的真实量测，导致部分目标被错误更新和漏估计，因此，该类方法的目标状态及数目估计精度较低。此外，如果跟踪场景中的杂波均值较大且检测概率较低时，该类方法的滤波精度将进一步下降。At present, the probability hypothesis density filtering method based on the Gaussian mixture (Gaussian mixture, GM) approximation method has been verified in practical applications. In the clutter tracking environment, the GM-PHD filter is widely used in the target tracking system of the linear Gaussian dynamic model because of its advantages of high iteration efficiency and convenient state extraction. However, the multi-target tracking method based on PHD filtering assumes that the distance between the targets in the tracking scene is relatively long, that is, there is no mutual interference between the targets; The distances can often be very small, ie in close proximity to targets (cross-moving targets and parallel-moving targets). When multiple targets in the tracking scene are close to each other or keep moving at close range, the multi-target tracking method based on PHD filtering cannot correctly distinguish the real measurement from each target itself, resulting in some targets being updated incorrectly and Therefore, the target state and number estimation accuracy of this type of method is low. In addition, if the average value of clutter in the tracking scene is large and the detection probability is low, the filtering accuracy of this type of method will be further reduced.

发明内容Contents of the invention

针对平行运动目标场景中基于PHD滤波的多目标跟踪方法的目标状态及数目估计精度较低的问题，本发明提出了一种基于高斯混合概率假设密度的紧邻多目标跟踪方法，采用紧邻多目标高斯混合概率假设密度(MCST-GM-PHD)解决了密集杂波、较低检测概率跟踪环境下的平行运动目标跟踪问题。Aiming at the problem of low target state and number estimation accuracy of the multi-target tracking method based on PHD filtering in the parallel moving target scene, the present invention proposes a close-by multi-target tracking method based on Gaussian mixture probability hypothesis density, using the close-by multi-target Gaussian Mixed Probabilistic Hypothesis Density (MCST-GM-PHD) solves the problem of parallel moving target tracking in dense clutter and low detection probability tracking environment.

为解决以上技术问题，本发明所采用的技术方案如下：In order to solve the above technical problems, the technical scheme adopted in the present invention is as follows:

一种基于高斯混合概率假设密度的紧邻多目标跟踪方法，包括如下步骤：A method for tracking multiple targets in close proximity based on Gaussian mixture probability hypothesis density, comprising the following steps:

S1，增加高斯分量的标签和历史状态矩阵为辅助参数以构建用于表示目标的高斯分量的新标准描述集；S1, adding the label of the Gaussian component and the historical state matrix as auxiliary parameters to construct a new standard description set for the Gaussian component representing the target;

S2，初始化目标概率假设密度、目标标签集及目标历史状态矩阵集；S2, initialize the target probability hypothesis density, the target label set and the target historical state matrix set;

S3，根据新生目标的概率假设密度、标签集、历史状态矩阵集和存活目标的预测概率假设密度、预测标签集、预测历史状态矩阵集，计算目标预测概率假设密度、目标预测标签集、目标预测历史状态矩阵集；S3, according to the probability hypothesis density, label set, historical state matrix set of the newborn target, and the predicted probability hypothesis density, predicted label set, and predicted historical state matrix set of the surviving target, calculate the target prediction probability hypothesis density, target prediction label set, and target prediction Historical state matrix set;

S4，基于量测集计算目标后验概率假设密度、目标后验标签集和目标后验历史状态矩阵集，重分配目标后验概率假设密度中各高斯分量的权值；S4. Calculate the target posterior probability hypothesis density, the target posterior label set and the target posterior historical state matrix set based on the measurement set, and redistribute the weights of each Gaussian component in the target posterior probability hypothesis density;

S5，对目标的高斯分量集及其参数集进行变换，并对变换后的高斯分量集进行约简；S5, transforming the target Gaussian component set and its parameter set, and reducing the transformed Gaussian component set;

S6，估计目标的状态和数目；S6, estimating the state and number of targets;

S7，若跟踪单一时刻，则目标跟踪结束；若跟踪若干个时刻，则重复执行S3-S6直至迭代所有时刻。S7. If a single moment is tracked, the target tracking ends; if several moments are tracked, S3-S6 is repeatedly executed until all moments are iterated.

在步骤S1中，所述表示目标的高斯分量的新标准描述集的表达式为：In step S1, the expression of the new standard description set representing the Gaussian component of the target is:

o＝{w,m,P,l,χ}；o={w,m,P,l,χ};

式中，w表示高斯分量的权值，m表示高斯分量的均值，P表示高斯分量的协方差矩阵，l表示高斯分量的标签，χ表示高斯分量的历史状态矩阵；In the formula, w represents the weight of the Gaussian component, m represents the mean value of the Gaussian component, P represents the covariance matrix of the Gaussian component, l represents the label of the Gaussian component, and χ represents the historical state matrix of the Gaussian component;

k时刻的高斯分量的历史状态矩阵χk的表达式为：The expression of the historical state matrix χ k of the Gaussian component at time k is:

χk＝[mk-δ+1,...,mk-1,mk]；χ k ＝[m k-δ+1 ,...,m k-1 ,m k ];

式中，δ表示传感器所设定的历史状态矩阵中的元素数目阈值。In the formula, δ represents the threshold number of elements in the historical state matrix set by the sensor.

在步骤S2中，所述目标概率假设密度

Figure BDA0002465416630000031
的表达式为：In step S2, the target probability hypothesis density
Figure BDA0002465416630000031
The expression is:

Figure BDA0002465416630000032
Figure BDA0002465416630000032

式中，

Figure BDA0002465416630000041
表示一个均值为m，协方差为P的高斯密度，x表示高斯分量o的状态，
Figure BDA0002465416630000042
表示k时刻第i个高斯分量
Figure BDA0002465416630000043
的权值，
Figure BDA0002465416630000044
表示k时刻第i个高斯分量
Figure BDA0002465416630000045
的均值，
Figure BDA0002465416630000046
表示k时刻第i个高斯分量
Figure BDA0002465416630000047
的协方差矩阵，Jk表示k时刻高斯分量的数目；In the formula,
Figure BDA0002465416630000041
Represents a Gaussian density with mean m and covariance P, x represents the state of Gaussian component o,
Figure BDA0002465416630000042
Indicates the i-th Gaussian component at time k
Figure BDA0002465416630000043
the weight of
Figure BDA0002465416630000044
Indicates the i-th Gaussian component at time k
Figure BDA0002465416630000045
the mean value of
Figure BDA0002465416630000046
Indicates the i-th Gaussian component at time k
Figure BDA0002465416630000047
The covariance matrix of , J k represents the number of Gaussian components at time k;

所述标签集

Figure BDA0002465416630000048
的表达式为：The tag set
Figure BDA0002465416630000048
The expression is:

Figure BDA0002465416630000049
Figure BDA0002465416630000049

式中，

Figure BDA00024654166300000410
表示k时刻第i个高斯分量
Figure BDA00024654166300000411
的标签；In the formula,
Figure BDA00024654166300000410
Indicates the i-th Gaussian component at time k
Figure BDA00024654166300000411
Tag of;

所述历史状态矩阵集Λk的表达式为：The expression of the historical state matrix set Λ k is:

Figure BDA00024654166300000412
Figure BDA00024654166300000412

式中，

Figure BDA00024654166300000413
表示k时刻第i个高斯分量
Figure BDA00024654166300000414
的历史状态矩阵，且
Figure BDA00024654166300000415
In the formula,
Figure BDA00024654166300000413
Indicates the i-th Gaussian component at time k
Figure BDA00024654166300000414
The historical state matrix of , and
Figure BDA00024654166300000415

在步骤S3中，所述新生目标的概率假设密度γk(x)的表达式为：In step S3, the expression of the probability hypothesis density γ k (x) of the newborn target is:

Figure BDA00024654166300000416
Figure BDA00024654166300000416

式中，Jγ,k表示新生高斯分量的数目，

Figure BDA00024654166300000417
表示k时刻第j个新生高斯分量
Figure BDA00024654166300000418
的权值，
Figure BDA00024654166300000419
表示k时刻第j个新生高斯分量
Figure BDA00024654166300000420
的均值，
Figure BDA00024654166300000421
表示k时刻第j个新生高斯分量
Figure BDA00024654166300000422
的协方差矩阵；In the formula, J γ,k represents the number of newborn Gaussian components,
Figure BDA00024654166300000417
Indicates the jth newborn Gaussian component at time k
Figure BDA00024654166300000418
the weight of
Figure BDA00024654166300000419
Indicates the jth newborn Gaussian component at time k
Figure BDA00024654166300000420
the mean value of
Figure BDA00024654166300000421
Indicates the jth newborn Gaussian component at time k
Figure BDA00024654166300000422
The covariance matrix of ;

所述新生目标的标签集

Figure BDA00024654166300000423
的表达式为：The tag set for the nascent target
Figure BDA00024654166300000423
The expression is:

Figure BDA00024654166300000424
Figure BDA00024654166300000424

式中，

Figure BDA00024654166300000425
表示第j个新生高斯分量
Figure BDA00024654166300000426
的标签；In the formula,
Figure BDA00024654166300000425
Indicates the jth nascent Gaussian component
Figure BDA00024654166300000426
Tag of;

所述新生目标的历史状态矩阵集Λγ,k的表达式为：The historical state matrix set Λ γ of the newborn target, the expression of k is:

Figure BDA00024654166300000427
Figure BDA00024654166300000427

式中，

Figure BDA00024654166300000428
表示第j个新生高斯分量
Figure BDA00024654166300000429
的历史状态矩阵，且
Figure BDA00024654166300000430
In the formula,
Figure BDA00024654166300000428
Indicates the jth nascent Gaussian component
Figure BDA00024654166300000429
The historical state matrix of , and
Figure BDA00024654166300000430

所述存活目标的预测概率假设密度

Figure BDA00024654166300000431
的表达式为：The predicted probability hypothesis density for the survival target
Figure BDA00024654166300000431
The expression is:

Figure BDA00024654166300000432
Figure BDA00024654166300000432

式中，

Figure BDA00024654166300000433
表示第i个存活高斯分量
Figure BDA00024654166300000434
的预测权值，
Figure BDA00024654166300000435
表示第i个存活高斯分量
Figure BDA00024654166300000436
的预测均值，
Figure BDA00024654166300000437
表示第i个存活高斯分量
Figure BDA00024654166300000438
的预测协方差矩阵，Js,k|k-1表示在k时刻用k-1时刻高斯分量数目Jk-1所预测的存活高斯分量的预测数目；In the formula,
Figure BDA00024654166300000433
Denotes the i-th surviving Gaussian component
Figure BDA00024654166300000434
the predictive weight of
Figure BDA00024654166300000435
Denotes the i-th surviving Gaussian component
Figure BDA00024654166300000436
the predicted mean of
Figure BDA00024654166300000437
Denotes the i-th surviving Gaussian component
Figure BDA00024654166300000438
The prediction covariance matrix of , J s,k|k-1 represents the predicted number of surviving Gaussian components predicted by the number of Gaussian components J k - 1 at time k-1 at time k;

所述存活目标的预测标签集

Figure BDA0002465416630000051
的表达式为：The predicted label set of the surviving target
Figure BDA0002465416630000051
The expression is:

Figure BDA0002465416630000052
Figure BDA0002465416630000052

式中，

Figure BDA0002465416630000053
Figure BDA0002465416630000054
表示k时刻第i个存活高斯分量
Figure BDA0002465416630000055
的预测标签，
Figure BDA0002465416630000056
表示k-1时刻第i个高斯分量
Figure BDA0002465416630000057
的标签；In the formula,
Figure BDA0002465416630000053
Figure BDA0002465416630000054
Indicates the i-th surviving Gaussian component at time k
Figure BDA0002465416630000055
the predicted label of
Figure BDA0002465416630000056
Represents the i-th Gaussian component at time k-1
Figure BDA0002465416630000057
Tag of;

所述存活目标的预测历史状态矩阵集Λs,k|k-1的表达式为：The expression of the predicted historical state matrix set Λ s,k|k-1 of the surviving target is:

Figure BDA0002465416630000058
Figure BDA0002465416630000058

式中，

Figure BDA0002465416630000059
表示k时刻第i个存活高斯分量
Figure BDA00024654166300000510
的预测历史状态矩阵；
Figure BDA00024654166300000511
Figure BDA00024654166300000512
表示k-1时刻第i个高斯分量
Figure BDA00024654166300000513
的历史状态矩阵
Figure BDA00024654166300000514
的第2列向量，
Figure BDA00024654166300000515
表示k-1时刻第i个高斯分量
Figure BDA00024654166300000516
的历史状态矩阵
Figure BDA00024654166300000517
的第δ列向量；In the formula,
Figure BDA0002465416630000059
Indicates the i-th surviving Gaussian component at time k
Figure BDA00024654166300000510
The predicted historical state matrix of ;
Figure BDA00024654166300000511
Figure BDA00024654166300000512
Represents the i-th Gaussian component at time k-1
Figure BDA00024654166300000513
The historical state matrix of
Figure BDA00024654166300000514
The 2nd column vector of ,
Figure BDA00024654166300000515
Represents the i-th Gaussian component at time k-1
Figure BDA00024654166300000516
The historical state matrix of
Figure BDA00024654166300000517
The δth column vector of ;

所述目标预测概率假设密度

Figure BDA00024654166300000518
的表达式为：The target predicted probability hypothesis density
Figure BDA00024654166300000518
The expression is:

Figure BDA00024654166300000519
Figure BDA00024654166300000519

式中，Jk|k-1表示预测高斯分量的预测数目，

Figure BDA00024654166300000520
表示第i个预测高斯分量
Figure BDA00024654166300000521
的预测权值，
Figure BDA00024654166300000522
表示第i个预测高斯分量
Figure BDA00024654166300000523
的预测均值，
Figure BDA00024654166300000524
表示第i个预测高斯分量
Figure BDA00024654166300000525
的预测协方差矩阵；In the formula, J k|k-1 represents the predicted number of predicted Gaussian components,
Figure BDA00024654166300000520
Indicates the i-th predicted Gaussian component
Figure BDA00024654166300000521
the predictive weight of
Figure BDA00024654166300000522
Indicates the i-th predicted Gaussian component
Figure BDA00024654166300000523
the predicted mean of
Figure BDA00024654166300000524
Indicates the i-th predicted Gaussian component
Figure BDA00024654166300000525
The prediction covariance matrix of ;

所述目标预测标签集

Figure BDA00024654166300000526
的表达式为：The target prediction label set
Figure BDA00024654166300000526
The expression is:

Figure BDA00024654166300000527
Figure BDA00024654166300000527

式中，

Figure BDA00024654166300000528
表示第i个预测高斯分量
Figure BDA00024654166300000529
的预测标签；In the formula,
Figure BDA00024654166300000528
Indicates the i-th predicted Gaussian component
Figure BDA00024654166300000529
the predicted label;

所述目标预测历史状态矩阵集Λk|k-1的表达式为：The expression of the target prediction historical state matrix set Λ k|k-1 is:

Figure BDA00024654166300000530
Figure BDA00024654166300000530

式中，

Figure BDA00024654166300000531
表示第i个预测高斯分量
Figure BDA00024654166300000532
的预测历史状态矩阵。In the formula,
Figure BDA00024654166300000531
Indicates the i-th predicted Gaussian component
Figure BDA00024654166300000532
The predicted history state matrix of .

在步骤S4中，所述量测集Zk的表达式为：In step S4, the expression of the measurement set Z k is:

Figure BDA00024654166300000533
Figure BDA00024654166300000533

式中，Mk表示k时刻量测集Zk中量测的数目，

Figure BDA00024654166300000534
表示量测集Zk中的第j个量测；In the formula, M k represents the number of measurements in the measurement set Z k at time k,
Figure BDA00024654166300000534
Indicates the jth measurement in the measurement set Z k ;

所述计算目标后验概率假设密度

Figure BDA0002465416630000061
目标后验标签集
Figure BDA0002465416630000062
和目标后验历史状态矩阵集Λk，包括如下步骤：The computed target posterior probability hypothesis density
Figure BDA0002465416630000061
target posterior label set
Figure BDA0002465416630000062
and the target posterior historical state matrix set Λ k , including the following steps:

S4.1；计算高斯分量

Figure BDA0002465416630000063
的权值
Figure BDA0002465416630000064
均值
Figure BDA0002465416630000065
协方差矩阵
Figure BDA0002465416630000066
标签
Figure BDA0002465416630000067
历史状态矩阵
Figure BDA0002465416630000068
S4.1; Calculation of Gaussian components
Figure BDA0002465416630000063
weight of
Figure BDA0002465416630000064
average
Figure BDA0002465416630000065
covariance matrix
Figure BDA0002465416630000066
Label
Figure BDA0002465416630000067
Historical State Matrix
Figure BDA0002465416630000068

所述高斯分量

Figure BDA0002465416630000069
的权值
Figure BDA00024654166300000610
的表达式为：The Gaussian component
Figure BDA0002465416630000069
weight of
Figure BDA00024654166300000610
The expression is:

Figure BDA00024654166300000611
Figure BDA00024654166300000611

式中，

Figure BDA00024654166300000612
表示基于量测
Figure BDA00024654166300000613
的杂波强度，pd表示检测概率，Hk表示k时刻量测矩阵；Rk表示k时刻量测噪声协方差矩阵，
Figure BDA00024654166300000614
表示预测高斯分量
Figure BDA00024654166300000615
的预测权值，
Figure BDA00024654166300000616
表示预测高斯分量
Figure BDA00024654166300000617
的预测均值，
Figure BDA00024654166300000618
表示预测高斯分量
Figure BDA00024654166300000619
的预测协方差矩阵；In the formula,
Figure BDA00024654166300000612
Indicates based on measurement
Figure BDA00024654166300000613
clutter intensity, p d represents the detection probability, H k represents the measurement matrix at time k; R k represents the measurement noise covariance matrix at time k,
Figure BDA00024654166300000614
represents the predicted Gaussian component
Figure BDA00024654166300000615
the predictive weight of
Figure BDA00024654166300000616
represents the predicted Gaussian component
Figure BDA00024654166300000617
the predicted mean of
Figure BDA00024654166300000618
represents the predicted Gaussian component
Figure BDA00024654166300000619
The prediction covariance matrix of ;

所述高斯分量

Figure BDA00024654166300000620
的均值
Figure BDA00024654166300000621
的表达式为：The Gaussian component
Figure BDA00024654166300000620
mean of
Figure BDA00024654166300000621
The expression is:

Figure BDA00024654166300000622
Figure BDA00024654166300000622

式中，

Figure BDA00024654166300000623
表示高斯分量
Figure BDA00024654166300000624
的信息增益，且
Figure BDA00024654166300000625
In the formula,
Figure BDA00024654166300000623
Represents the Gaussian component
Figure BDA00024654166300000624
information gain, and
Figure BDA00024654166300000625

所述高斯分量

Figure BDA00024654166300000626
的协方差矩阵
Figure BDA00024654166300000627
的表达式为：The Gaussian component
Figure BDA00024654166300000626
The covariance matrix of
Figure BDA00024654166300000627
The expression is:

Figure BDA00024654166300000628
Figure BDA00024654166300000628

式中，I表示单位矩阵；In the formula, I represents the identity matrix;

所述高斯分量

Figure BDA00024654166300000629
的标签
Figure BDA00024654166300000630
的表达式为：The Gaussian component
Figure BDA00024654166300000629
Tag of
Figure BDA00024654166300000630
The expression is:

Figure BDA00024654166300000631
Figure BDA00024654166300000631

所述高斯分量

Figure BDA00024654166300000632
的历史状态矩阵
Figure BDA00024654166300000633
的表达式为：The Gaussian component
Figure BDA00024654166300000632
The historical state matrix of
Figure BDA00024654166300000633
The expression is:

Figure BDA00024654166300000634
Figure BDA00024654166300000634

式中，

Figure BDA00024654166300000635
表示预测高斯分量
Figure BDA00024654166300000636
的预测历史状态矩阵
Figure BDA00024654166300000637
的第1列向量，
Figure BDA00024654166300000638
表示预测高斯分量
Figure BDA00024654166300000639
的预测历史状态矩阵
Figure BDA00024654166300000640
的第δ-1列向量，
Figure BDA00024654166300000641
表示高斯分量
Figure BDA00024654166300000642
的均值；In the formula,
Figure BDA00024654166300000635
represents the predicted Gaussian component
Figure BDA00024654166300000636
The forecast history state matrix of
Figure BDA00024654166300000637
The first column vector of ,
Figure BDA00024654166300000638
represents the predicted Gaussian component
Figure BDA00024654166300000639
The forecast history state matrix of
Figure BDA00024654166300000640
The δ-1th column vector of ,
Figure BDA00024654166300000641
Represents the Gaussian component
Figure BDA00024654166300000642
the mean value of

S4.2，计算高斯分量

Figure BDA00024654166300000643
所对应的非归一化权值矩阵Ak和归一化权值矩阵Bk，以对各高斯分量的权值进行再分配，输出目标后验概率假设密度
Figure BDA00024654166300000644
目标后验标签集
Figure BDA00024654166300000645
和目标后验历史状态矩阵集Λk；S4.2, Calculation of Gaussian components
Figure BDA00024654166300000643
The corresponding unnormalized weight matrix A k and normalized weight matrix B k are used to redistribute the weights of each Gaussian component, and output the target posterior probability hypothesis density
Figure BDA00024654166300000644
target posterior label set
Figure BDA00024654166300000645
and the target posterior history state matrix set Λ k ;

所述非归一化权值矩阵Ak的表达式为：The expression of the non-normalized weight matrix A k is:

Figure BDA0002465416630000071
Figure BDA0002465416630000071

式中，

Figure BDA0002465416630000072
表示高斯分量
Figure BDA0002465416630000073
的非归一化权值，且
Figure BDA0002465416630000074
In the formula,
Figure BDA0002465416630000072
Represents the Gaussian component
Figure BDA0002465416630000073
The unnormalized weights of , and
Figure BDA0002465416630000074

归一化权值矩阵Bk的表达式为：The expression of the normalized weight matrix B k is:

Figure BDA0002465416630000075
Figure BDA0002465416630000075

式中，

Figure BDA0002465416630000076
表示高斯分量
Figure BDA0002465416630000077
的权值。In the formula,
Figure BDA0002465416630000076
Represents the Gaussian component
Figure BDA0002465416630000077
weights.

在步骤S4.2中，所述对各高斯分量的权值进行再分配，输出目标后验概率假设密度

Figure BDA0002465416630000078
目标后验标签集
Figure BDA0002465416630000079
和目标后验历史状态矩阵集Λk包括如下步骤：In step S4.2, the weights of each Gaussian component are redistributed, and the target posterior probability hypothesis density is output
Figure BDA0002465416630000078
target posterior label set
Figure BDA0002465416630000079
and the target posterior historical state matrix set Λ k include the following steps:

S4.2.1，查找归一化权值矩阵Bk中的最大权值的索引<i*,j*>，构建与该最大权值高斯分量具有相同标签的分量索引集Ψ，计算分量索引集Ψ中索引所对应的高斯分量的权值和ηw；S4.2.1, find the index <i * , j * > of the maximum weight in the normalized weight matrix B k , construct a component index set Ψ with the same label as the maximum weight Gaussian component, and calculate the component index set Ψ The weight sum η w of the Gaussian component corresponding to the index in ;

所述最大权值的索引<i*,j*>的表达式为：The expression of the index <i * , j * > of the maximum weight is:

Figure BDA00024654166300000710
Figure BDA00024654166300000710

式中，

Figure BDA00024654166300000711
为高斯分量索引集，且其初始值为
Figure BDA00024654166300000712
Mk表示量测集Zk中量测的数目；In the formula,
Figure BDA00024654166300000711
is the Gaussian component index set, and its initial value is
Figure BDA00024654166300000712
M k represents the number of measurements in the measurement set Z k ;

所述分量索引集Ψ的表达式为：The expression of the component index set Ψ is:

Figure BDA00024654166300000713
Figure BDA00024654166300000713

式中，

Figure BDA00024654166300000714
表示高斯分量
Figure BDA00024654166300000715
的标签，
Figure BDA00024654166300000716
表示高斯分量
Figure BDA00024654166300000717
的标签；In the formula,
Figure BDA00024654166300000714
Represents the Gaussian component
Figure BDA00024654166300000715
Tag of,
Figure BDA00024654166300000716
Represents the Gaussian component
Figure BDA00024654166300000717
Tag of;

所述权值和ηw的表达式为：The expression of described weight and η w is:

Figure BDA00024654166300000718
Figure BDA00024654166300000718

S4.2.2，计算标志位

Figure BDA00024654166300000719
如果标志位
Figure BDA00024654166300000720
则更新分量索引集Ψ中索引所对应的高斯分量的权值和ηw和标志位
Figure BDA00024654166300000721
若标志位
Figure BDA00024654166300000722
则执行步骤S4.2.3；S4.2.2, Calculation flag bit
Figure BDA00024654166300000719
if flag
Figure BDA00024654166300000720
Then update the weight and η w and the flag bit of the Gaussian component corresponding to the index in the component index set Ψ
Figure BDA00024654166300000721
if flag
Figure BDA00024654166300000722
Then execute step S4.2.3;

所述标志位

Figure BDA00024654166300000723
的表达式为：The flag bit
Figure BDA00024654166300000723
The expression is:

Figure BDA00024654166300000724
Figure BDA00024654166300000724

S4.2.3，将归一化权值矩阵Bk中的权值

Figure BDA0002465416630000081
拷贝到优化权值矩阵Ek中的对应位置，其中，i∈Ψ、j＝1:Mk；S4.2.3, normalize the weights in the weight matrix B k
Figure BDA0002465416630000081
Copy to the corresponding position in the optimization weight matrix E k , wherein, i∈Ψ, j=1:M k ;

S4.2.4，更新高斯分量索引集

Figure BDA0002465416630000082
如果高斯分量索引集
Figure BDA0002465416630000083
为空，则继续执行步骤S4.2.5，否则返回执行步骤S4.2.1；S4.2.4, update Gaussian component index set
Figure BDA0002465416630000082
If the Gaussian component index set
Figure BDA0002465416630000083
If it is empty, continue to execute step S4.2.5, otherwise return to execute step S4.2.1;

S4.2.5，基于优化权值矩阵Ek中的权值，更新目标后验概率假设密度

Figure BDA0002465416630000084
中的相应高斯分量的权值；输出目标后验概率假设密度
Figure BDA0002465416630000085
目标后验标签集
Figure BDA0002465416630000086
和目标后验历史状态矩阵集Λk；S4.2.5, update the target posterior probability hypothesis density based on the weights in the optimized weight matrix E k
Figure BDA0002465416630000084
The weights of the corresponding Gaussian components in ; the output target posterior probability hypothesis density
Figure BDA0002465416630000085
target posterior label set
Figure BDA0002465416630000086
and the target posterior history state matrix set Λ k ;

所述目标后验概率假设密度

Figure BDA0002465416630000087
的表达式为：The target posterior probability hypothesis density
Figure BDA0002465416630000087
The expression is:

Figure BDA0002465416630000088
Figure BDA0002465416630000088

所述目标后验标签集

Figure BDA0002465416630000089
的表达式为：The target posterior label set
Figure BDA0002465416630000089
The expression is:

Figure BDA00024654166300000810
Figure BDA00024654166300000810

所述目标后验历史状态矩阵集Λk的表达式为：The expression of the target posterior history state matrix set Λ k is:

Figure BDA00024654166300000811
Figure BDA00024654166300000811

在步骤S4.2.2中，所述更新分量索引集中索引所对应的高斯分量的权值和ηw和标志位

Figure BDA00024654166300000812
包括如下步骤：In step S4.2.2, the weight sum η w and flag bit of the Gaussian component corresponding to the index in the update component index set
Figure BDA00024654166300000812
Including the following steps:

S4.2.2a，从具有相同标签

Figure BDA00024654166300000813
的高斯分量中选择具有最小加权Hungarian距离的高斯分量；S4.2.2a, from the same label
Figure BDA00024654166300000813
Select the Gaussian component with the smallest weighted Hungarian distance among the Gaussian components of ;

所述高斯分量所对应的索引<ir,jc>的表达式为：The expression of the index <i r , j c > corresponding to the Gaussian component is:

Figure BDA00024654166300000814
Figure BDA00024654166300000814

其中，

Figure BDA00024654166300000815
in,
Figure BDA00024654166300000815

式中，比例系数ζ＝[1,δ-1/δ,δ-2/δ,δ-3/δ,δ-4/δ]，

Figure BDA00024654166300000816
表示高斯分量
Figure BDA00024654166300000817
在k时刻的历史状态矩阵
Figure BDA00024654166300000818
的第l列向量，
Figure BDA00024654166300000819
表示
Figure BDA00024654166300000820
与量测
Figure BDA00024654166300000821
间的Hungarian距离，其中，
Figure BDA00024654166300000822
In the formula, the proportional coefficient ζ=[1, δ-1/δ, δ-2/δ, δ-3/δ, δ-4/δ],
Figure BDA00024654166300000816
Represents the Gaussian component
Figure BDA00024654166300000817
Historical state matrix at time k
Figure BDA00024654166300000818
The l-th column of the vector,
Figure BDA00024654166300000819
express
Figure BDA00024654166300000820
and measurement
Figure BDA00024654166300000821
The Hungarian distance between, where,
Figure BDA00024654166300000822

S4.2.2b，更新非归一化权值矩阵Ak和归一化权值矩阵Bk中的各权值，对应的表达式分别为：S4.2.2b, update the weights in the unnormalized weight matrix A k and the normalized weight matrix B k , the corresponding expressions are respectively:

Figure BDA0002465416630000091
Figure BDA0002465416630000091

式中，比例因子

Figure BDA0002465416630000092
Figure BDA0002465416630000093
表示高斯分量
Figure BDA0002465416630000094
的标签；In the formula, the scale factor
Figure BDA0002465416630000092
Figure BDA0002465416630000093
Represents the Gaussian component
Figure BDA0002465416630000094
Tag of;

Figure BDA0002465416630000095
Figure BDA0002465416630000095

S4.2.2c，更新分量索引集Ψ中索引所对应的高斯分量的权值和ηw和标志位

Figure BDA0002465416630000096
如果标志位
Figure BDA0002465416630000097
则返回执行步骤S4.2.2b，若标志位
Figure BDA0002465416630000098
则执行步骤S4.2.3。S4.2.2c, update the weight and η w and flag bit of the Gaussian component corresponding to the index in the component index set Ψ
Figure BDA0002465416630000096
if flag
Figure BDA0002465416630000097
Then return to step S4.2.2b, if the flag
Figure BDA0002465416630000098
Then execute step S4.2.3.

在步骤S5中，所述目标的高斯分量集的表达式为：In step S5, the expression of the Gaussian component set of the target is:

Figure BDA0002465416630000099
Figure BDA0002465416630000099

式中，Jk|k-1表示预测高斯分量的预测数目，Mk表示量测集Zk中量测的数目；In the formula, J k|k-1 represents the predicted number of predicted Gaussian components, and M k represents the number of measurements in the measurement set Z k ;

所述参数集的表达式为：The expression of the parameter set is:

Figure BDA00024654166300000910
Figure BDA00024654166300000910

式中，

Figure BDA00024654166300000911
表示预测高斯分量
Figure BDA00024654166300000912
的预测权值，
Figure BDA00024654166300000913
表示预测高斯分量
Figure BDA00024654166300000914
的预测均值，
Figure BDA00024654166300000915
表示预测高斯分量
Figure BDA00024654166300000916
的预测协方差矩阵，
Figure BDA00024654166300000917
表示预测高斯分量
Figure BDA00024654166300000918
的预测标签，
Figure BDA00024654166300000919
表示预测高斯分量
Figure BDA00024654166300000920
的预测历史状态矩阵，
Figure BDA00024654166300000921
表示高斯分量
Figure BDA00024654166300000922
的权值，
Figure BDA00024654166300000923
表示高斯分量
Figure BDA00024654166300000924
的均值，
Figure BDA00024654166300000925
表示高斯分量
Figure BDA00024654166300000926
的协方差矩阵，
Figure BDA00024654166300000927
表示高斯分量
Figure BDA00024654166300000928
的标签，
Figure BDA00024654166300000929
表示高斯分量
Figure BDA00024654166300000930
的历史状态矩阵；In the formula,
Figure BDA00024654166300000911
represents the predicted Gaussian component
Figure BDA00024654166300000912
the predictive weight of
Figure BDA00024654166300000913
represents the predicted Gaussian component
Figure BDA00024654166300000914
the predicted mean of
Figure BDA00024654166300000915
represents the predicted Gaussian component
Figure BDA00024654166300000916
The prediction covariance matrix of ,
Figure BDA00024654166300000917
represents the predicted Gaussian component
Figure BDA00024654166300000918
the predicted label of
Figure BDA00024654166300000919
represents the predicted Gaussian component
Figure BDA00024654166300000920
The predicted history state matrix of ,
Figure BDA00024654166300000921
Represents the Gaussian component
Figure BDA00024654166300000922
the weight of
Figure BDA00024654166300000923
Represents the Gaussian component
Figure BDA00024654166300000924
the mean value of
Figure BDA00024654166300000925
Represents the Gaussian component
Figure BDA00024654166300000926
The covariance matrix of ,
Figure BDA00024654166300000927
Represents the Gaussian component
Figure BDA00024654166300000928
Tag of,
Figure BDA00024654166300000929
Represents the Gaussian component
Figure BDA00024654166300000930
The historical state matrix of ;

所述变换后的高斯分量集的表达式为：The expression of the transformed Gaussian component set is:

Figure BDA00024654166300000931
Figure BDA00024654166300000931

式中，高斯分量数目为Jk＝Jk|k-1+Jk|k-1×Mk；In the formula, the number of Gaussian components is J k ＝J k|k-1 +J k|k-1 ×M k ;

所述变换后的高斯分量集所对应的参数集表达式为：The parameter set expression corresponding to the transformed Gaussian component set is:

Figure BDA00024654166300000932
Figure BDA00024654166300000932

所述对变换后的高斯分量集进行约简包括步骤如下：The step of reducing the transformed Gaussian component set includes the following steps:

S5.1，设定删减阈值T1，融合阈值U，最大高斯分量数目阈值Jmax；S5.1, set the pruning threshold T 1 , the fusion threshold U, the maximum Gaussian component number threshold J max ;

S5.2，设定计数变量j＝0和高斯分量数目变量

Figure BDA00024654166300000933
高斯分量索引集
Figure BDA00024654166300000934
S5.2, set count variable j=0 and Gaussian component number variable
Figure BDA00024654166300000933
Gaussian component index set
Figure BDA00024654166300000934

式中，

Figure BDA00024654166300000935
表示高斯分量
Figure BDA00024654166300000936
的权值。In the formula,
Figure BDA00024654166300000935
Represents the Gaussian component
Figure BDA00024654166300000936
weights.

S5.3，执行j＝j+1，筛选具有最大权值的高斯分量

Figure BDA0002465416630000101
以建立新的高斯分量；S5.3, execute j=j+1, and filter the Gaussian component with the largest weight
Figure BDA0002465416630000101
to create a new Gaussian component;

所述最大权值的高斯分量

Figure BDA0002465416630000102
的索引l*的表达式为：the Gaussian component of the maximum weight
Figure BDA0002465416630000102
The expression for the index l * is:

Figure BDA0002465416630000103
Figure BDA0002465416630000103

S5.4，更新高斯分量索引集

Figure BDA0002465416630000104
若高斯分量索引集
Figure BDA0002465416630000105
不为空，则返回执行步骤S5.3；若高斯分量索引集
Figure BDA0002465416630000106
为空，更新高斯分量数目变量
Figure BDA0002465416630000107
且执行步骤S5.5；S5.4, update Gaussian component index set
Figure BDA0002465416630000104
If the Gaussian component index set
Figure BDA0002465416630000105
is not empty, return to step S5.3; if Gaussian component index set
Figure BDA0002465416630000106
If it is empty, update the Gaussian component number variable
Figure BDA0002465416630000107
And execute step S5.5;

所述更新高斯分量索引集

Figure BDA0002465416630000108
的表达式为：The updated Gaussian component index set
Figure BDA0002465416630000108
The expression is:

Figure BDA0002465416630000109
Figure BDA0002465416630000109

式中，过渡索引集

Figure BDA00024654166300001010
Figure BDA00024654166300001011
表示最大权值的高斯分量
Figure BDA00024654166300001012
的标签，
Figure BDA00024654166300001013
表示高斯分量
Figure BDA00024654166300001014
的标签。In the formula, the transition index set
Figure BDA00024654166300001010
Figure BDA00024654166300001011
Gaussian component representing the maximum weight
Figure BDA00024654166300001012
Tag of,
Figure BDA00024654166300001013
Represents the Gaussian component
Figure BDA00024654166300001014
Tag of.

所述更新高斯分量数目变量

Figure BDA00024654166300001015
的表达式为：The updated Gaussian component number variable
Figure BDA00024654166300001015
The expression is:

Figure BDA00024654166300001016
Figure BDA00024654166300001016

S5.5，对高斯分量数目变量

Figure BDA00024654166300001017
和最大高斯分量数目阈值Jmax的值进行比较，根据新的高斯分量集
Figure BDA00024654166300001018
获得约简后的高斯分量集
Figure BDA00024654166300001019
S5.5, for the number of Gaussian components variable
Figure BDA00024654166300001017
Compared with the value of the maximum Gaussian component number threshold J max , according to the new Gaussian component set
Figure BDA00024654166300001018
Obtain the reduced Gaussian component set
Figure BDA00024654166300001019

如果

Figure BDA00024654166300001020
按权值
Figure BDA00024654166300001021
由大到小的顺序对所获得的新的高斯分量集
Figure BDA00024654166300001022
进行排列，取前Jmax个高斯分量构建约简后的高斯分量集
Figure BDA00024654166300001023
其中
Figure BDA00024654166300001024
Jk＝Jmax；若
Figure BDA00024654166300001025
则新的高斯分量集
Figure BDA00024654166300001026
为约简后的高斯分量集
Figure BDA00024654166300001027
其中
Figure BDA00024654166300001028
if
Figure BDA00024654166300001020
by weight
Figure BDA00024654166300001021
The new set of Gaussian components obtained by ordering from large to small
Figure BDA00024654166300001022
Arrange and take the first J max Gaussian components to construct the reduced Gaussian component set
Figure BDA00024654166300001023
in
Figure BDA00024654166300001024
J k = J max ; if
Figure BDA00024654166300001025
Then the new set of Gaussian components
Figure BDA00024654166300001026
is the reduced Gaussian component set
Figure BDA00024654166300001027
in
Figure BDA00024654166300001028

在步骤S5.3中，所述建立新的高斯分量包括如下步骤：In step S5.3, the establishment of a new Gaussian component includes the following steps:

S5.3.1，定义过渡索引集

Figure BDA00024654166300001029
S5.3.1, Define Transition Index Sets
Figure BDA00024654166300001029

式中，

Figure BDA00024654166300001030
表示最大权值的高斯分量
Figure BDA00024654166300001031
的标签；In the formula,
Figure BDA00024654166300001030
Gaussian component representing the maximum weight
Figure BDA00024654166300001031
Tag of;

S5.3.2，定义过渡索引集

Figure BDA00024654166300001032
S5.3.2, Define Transition Index Sets
Figure BDA00024654166300001032

式中，

Figure BDA00024654166300001033
表示最大权值的高斯分量
Figure BDA00024654166300001034
的均值，
Figure BDA00024654166300001035
表示最大权值的高斯分量
Figure BDA00024654166300001036
的协方差矩阵，
Figure BDA00024654166300001037
表示高斯分量
Figure BDA00024654166300001038
的均值；In the formula,
Figure BDA00024654166300001033
Gaussian component representing the maximum weight
Figure BDA00024654166300001034
the mean value of
Figure BDA00024654166300001035
Gaussian component representing the maximum weight
Figure BDA00024654166300001036
The covariance matrix of ,
Figure BDA00024654166300001037
Represents the Gaussian component
Figure BDA00024654166300001038
the mean value of

S5.3.3，将过渡索引集L2中索引所对应的高斯分量

Figure BDA00024654166300001039
合并为一个新的高斯分量
Figure BDA00024654166300001040
S5.3.3, the Gaussian component corresponding to the index in the transition index set L2
Figure BDA00024654166300001039
combined into a new Gaussian component
Figure BDA00024654166300001040

所述新的高斯分量

Figure BDA00024654166300001041
的权值
Figure BDA00024654166300001042
的表达式为：The new Gaussian component
Figure BDA00024654166300001041
weight of
Figure BDA00024654166300001042
The expression is:

Figure BDA00024654166300001043
Figure BDA00024654166300001043

式中，

Figure BDA00024654166300001044
表示高斯分量
Figure BDA00024654166300001045
的权值；In the formula,
Figure BDA00024654166300001044
Represents the Gaussian component
Figure BDA00024654166300001045
the weight of

所述新的高斯分量

Figure BDA0002465416630000111
的均值
Figure BDA0002465416630000112
的表达式为：The new Gaussian component
Figure BDA0002465416630000111
mean of
Figure BDA0002465416630000112
The expression is:

Figure BDA0002465416630000113
Figure BDA0002465416630000113

所述新的高斯分量

Figure BDA0002465416630000114
的协方差矩阵
Figure BDA0002465416630000115
的表达式为：The new Gaussian component
Figure BDA0002465416630000114
The covariance matrix of
Figure BDA0002465416630000115
The expression is:

Figure BDA0002465416630000116
Figure BDA0002465416630000116

式中，

Figure BDA0002465416630000117
表示最大权值的高斯分量
Figure BDA0002465416630000118
的均值，
Figure BDA0002465416630000119
表示高斯分量
Figure BDA00024654166300001110
的协方差矩阵；In the formula,
Figure BDA0002465416630000117
Gaussian component representing the maximum weight
Figure BDA0002465416630000118
the mean value of
Figure BDA0002465416630000119
Represents the Gaussian component
Figure BDA00024654166300001110
The covariance matrix of ;

所述新的高斯分量

Figure BDA00024654166300001111
的标签
Figure BDA00024654166300001112
的表达式为：The new Gaussian component
Figure BDA00024654166300001111
Tag of
Figure BDA00024654166300001112
The expression is:

Figure BDA00024654166300001113
Figure BDA00024654166300001113

所述新的高斯分量

Figure BDA00024654166300001114
的历史状态矩阵
Figure BDA00024654166300001115
的表达式为：The new Gaussian component
Figure BDA00024654166300001114
The historical state matrix of
Figure BDA00024654166300001115
The expression is:

Figure BDA00024654166300001116
Figure BDA00024654166300001116

式中，

Figure BDA00024654166300001117
表示最大权值的高斯分量
Figure BDA00024654166300001118
的历史状态矩阵
Figure BDA00024654166300001119
的第1列向量，
Figure BDA00024654166300001120
表示最大权值的高斯分量
Figure BDA00024654166300001121
的历史状态矩阵
Figure BDA00024654166300001122
的第δ-1列向量。In the formula,
Figure BDA00024654166300001117
Gaussian component representing the maximum weight
Figure BDA00024654166300001118
The historical state matrix of
Figure BDA00024654166300001119
The first column vector of ,
Figure BDA00024654166300001120
Gaussian component representing the maximum weight
Figure BDA00024654166300001121
The historical state matrix of
Figure BDA00024654166300001122
The δ-1th column vector of .

在步骤S6中，所述估计目标的状态和数目包括如下步骤：In step S6, said estimating the state and number of targets includes the following steps:

S6.1，根据步骤S5中所获得的高斯分量参数集中的权值估计目标数目；S6.1, estimating the number of targets according to the weights in the Gaussian component parameter set obtained in step S5;

所述目标数目Nk的表达式为：The expression of the target number N k is:

Figure BDA00024654166300001123
Figure BDA00024654166300001123

式中，

Figure BDA00024654166300001124
表示高斯分量
Figure BDA00024654166300001125
的权值，Jk表示k时刻高斯分量的数目；In the formula,
Figure BDA00024654166300001124
Represents the Gaussian component
Figure BDA00024654166300001125
The weight of , J k represents the number of Gaussian components at time k;

S6.2，从高斯分量参数集中选择权值大于0.5的索引，之后将索引所对应的高斯分量作为真实目标，最后输出高斯分量的均值即作为当前时刻的目标状态估计。S6.2. Select an index with a weight greater than 0.5 from the Gaussian component parameter set, then use the Gaussian component corresponding to the index as the real target, and finally output the mean value of the Gaussian component as the target state estimate at the current moment.

本发明的有益效果：Beneficial effects of the present invention:

本发明适用于航空和地面交通管制、移动机器人的道路规划和避障、无人机等系统的目标检测与跟踪，应用范围广；具有良好的跟踪性能和鲁棒性，可满足实际工程系统的设计需求，为密集杂波、较低检测概率跟踪环境下的紧邻多目标跟踪系统的设计提供了一种有效的方案。The present invention is suitable for target detection and tracking of systems such as aviation and ground traffic control, road planning and obstacle avoidance of mobile robots, and unmanned aerial vehicles, and has a wide range of applications; it has good tracking performance and robustness, and can meet the requirements of actual engineering systems. According to the design requirements, it provides an effective solution for the design of a close-by multi-target tracking system in a dense clutter and low detection probability tracking environment.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

图1是本发明MCST-GM-PHD的流程示意图。Fig. 1 is a schematic flow chart of MCST-GM-PHD of the present invention.

图2是本发明试验采用的杂波环境下含有目标真实运动轨迹及量测的场景示意图；Fig. 2 is a schematic diagram of a scene containing the real motion trajectory and measurement of the target under the clutter environment used in the test of the present invention;

图3是采用本发明MCST-GM-PHD与GM-PHD方法、P-GM-PHD方法、CP-GM-PHD方法以及IR-GM-PHD方法的平均OSPA距离的比较效果图。Fig. 3 is a comparison effect diagram of the average OSPA distance of the MCST-GM-PHD method of the present invention and the GM-PHD method, the P-GM-PHD method, the CP-GM-PHD method and the IR-GM-PHD method.

图4是采用本发明MCST-GM-PHD与GM-PHD方法、P-GM-PHD方法、CP-GM-PHD方法以及IR-GM-PHD方法的平均目标数目估计数的比较效果图。Fig. 4 is a comparison effect diagram of the average target number estimates using the MCST-GM-PHD method of the present invention and the GM-PHD method, the P-GM-PHD method, the CP-GM-PHD method and the IR-GM-PHD method.

图5是不同杂波均值环境下本发明MCST-GM-PHD与GM-PHD方法、P-GM-PHD方法、CP-GM-PHD方法以及IR-GM-PHD方法的平均OSPA距离的比较效果图。Fig. 5 is a comparative effect diagram of the average OSPA distance of the MCST-GM-PHD of the present invention and the GM-PHD method, the P-GM-PHD method, the CP-GM-PHD method and the IR-GM-PHD method under different clutter mean environments .

图6是不同杂波均值环境下本发明MCST-GM-PHD与GM-PHD方法、P-GM-PHD方法、CP-GM-PHD方法以及IR-GM-PHD方法的平均目标数目估计数的比较效果图。Fig. 6 is the comparison of the average target number estimates of MCST-GM-PHD of the present invention and GM-PHD method, P-GM-PHD method, CP-GM-PHD method and IR-GM-PHD method under different clutter mean environments renderings.

图7是不同检测概率环境下本发明MCST-GM-PHD与GM-PHD方法、P-GM-PHD方法、CP-GM-PHD方法以及IR-GM-PHD方法的平均OSPA距离的比较效果图。Fig. 7 is a comparison effect diagram of the average OSPA distance of the MCST-GM-PHD method of the present invention and the GM-PHD method, the P-GM-PHD method, the CP-GM-PHD method and the IR-GM-PHD method under different detection probability environments.

图8是不同检测概率环境下本发明MCST-GM-PHD与GM-PHD方法、P-GM-PHD方法、CP-GM-PHD方法以及IR-GM-PHD方法的平均目标数目估计数的比较效果图。Fig. 8 is the comparative effect of the average target number estimate number of MCST-GM-PHD of the present invention and GM-PHD method, P-GM-PHD method, CP-GM-PHD method and IR-GM-PHD method under different detection probability environments picture.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有付出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

一种基于高斯混合概率假设密度的紧邻多目标跟踪方法，如图1所示，包括如下步骤：A method for tracking multiple targets in close proximity based on Gaussian mixture probability hypothesis density, as shown in Figure 1, includes the following steps:

S1，增加高斯分量的标签和历史状态矩阵为辅助参数以构建用于表示目标的高斯分量的新标准描述集；S1, adding the label of the Gaussian component and the historical state matrix as auxiliary parameters to construct a new standard description set for the Gaussian component representing the target;

所述表示目标的高斯分量的新标准描述集o的表达式为：The expression of the new standard description set o representing the Gaussian component of the target is:

o＝{w,m,P,l,χ}；o={w,m,P,l,χ};

式中，w表示高斯分量的权值，m表示高斯分量的均值，P表示高斯分量的协方差矩阵，l表示高斯分量的标签，χ表示高斯分量的历史状态矩阵；In the formula, w represents the weight of the Gaussian component, m represents the mean value of the Gaussian component, P represents the covariance matrix of the Gaussian component, l represents the label of the Gaussian component, and χ represents the historical state matrix of the Gaussian component;

标签用于识别高斯分量的身份以及属于不同目标的高斯分量；历史状态矩阵存储了高斯分量的若干个历史状态，通过计算目标的各高斯分量的历史状态矩阵与不同量测间的距离，实现当前时刻高斯分量与目标的相对最优匹配；在滤波器对目标进行初始化时，每个目标一般只采用一个高斯分量来表示，但是在滤波迭代过程中，每个目标通常由多个高斯分量来表示；The tag is used to identify the identity of the Gaussian component and the Gaussian component belonging to different targets; the historical state matrix stores several historical states of the Gaussian component, by calculating the distance between the historical state matrix of each Gaussian component of the target and different measurements, the current The relative optimal matching between the Gaussian component and the target at any time; when the filter initializes the target, each target is generally represented by only one Gaussian component, but in the filtering iteration process, each target is usually represented by multiple Gaussian components ;

k时刻的高斯分量的历史状态矩阵χk的表达式为：The expression of the historical state matrix χ k of the Gaussian component at time k is:

χk＝[mk-δ+1,…,mk-1,mk]；χ k ＝[m k-δ+1 ,...,m k-1 ,m k ];

式中，δ表示传感器所设定的历史状态矩阵中的元素数目阈值。In the formula, δ represents the threshold number of elements in the historical state matrix set by the sensor.

S2，初始化目标概率假设密度、标签集及历史状态矩阵集；S2, initialize the target probability hypothesis density, label set and historical state matrix set;

所述目标概率假设密度

Figure BDA0002465416630000131
的表达式为：The target probability hypothesis density
Figure BDA0002465416630000131
The expression is:

Figure BDA0002465416630000132
Figure BDA0002465416630000132

式中，

Figure BDA0002465416630000133
表示均值为m，协方差为P的高斯密度，x表示高斯分量o的状态，
Figure BDA0002465416630000134
表示k时刻第i个高斯分量
Figure BDA0002465416630000135
的权值，
Figure BDA0002465416630000136
表示k时刻第i个高斯分量
Figure BDA0002465416630000137
的均值，
Figure BDA0002465416630000138
表示k时刻第i个高斯分量
Figure BDA0002465416630000139
的协方差矩阵，Jk表示k时刻高斯分量的数目；In the formula,
Figure BDA0002465416630000133
Represents the Gaussian density with mean m and covariance P, x represents the state of Gaussian component o,
Figure BDA0002465416630000134
Indicates the i-th Gaussian component at time k
Figure BDA0002465416630000135
the weight of
Figure BDA0002465416630000136
Indicates the i-th Gaussian component at time k
Figure BDA0002465416630000137
the mean value of
Figure BDA0002465416630000138
Indicates the i-th Gaussian component at time k
Figure BDA0002465416630000139
The covariance matrix of , J k represents the number of Gaussian components at time k;

所述目标标签集

Figure BDA00024654166300001310
的表达式为：The target label set
Figure BDA00024654166300001310
The expression is:

Figure BDA00024654166300001311
Figure BDA00024654166300001311

式中，

Figure BDA00024654166300001312
表示k时刻第i个高斯分量
Figure BDA00024654166300001313
的标签；In the formula,
Figure BDA00024654166300001312
Indicates the i-th Gaussian component at time k
Figure BDA00024654166300001313
Tag of;

所述目标历史状态矩阵集Λk的表达式为：The expression of the target historical state matrix set Λ k is:

Figure BDA00024654166300001314
Figure BDA00024654166300001314

式中，

Figure BDA00024654166300001315
表示k时刻第i个高斯分量
Figure BDA00024654166300001316
的历史状态矩阵，且
Figure BDA00024654166300001317
In the formula,
Figure BDA00024654166300001315
Indicates the i-th Gaussian component at time k
Figure BDA00024654166300001316
The historical state matrix of , and
Figure BDA00024654166300001317

初始化目标概率假设密度、目标标签集及目标历史状态矩阵集，为对将要跟踪的目标进行初始化。Initialize the target probability hypothesis density, target label set and target historical state matrix set to initialize the target to be tracked.

S3，根据新生目标的概率假设密度、标签集、历史状态矩阵集和存活目标的预测概率假设密度、预测标签集、预测历史状态矩阵集，计算目标预测概率假设密度、目标预测标签集、目标预测历史状态矩阵集；S3, according to the probability hypothesis density, label set, historical state matrix set of the newborn target, and the predicted probability hypothesis density, predicted label set, and predicted historical state matrix set of the surviving target, calculate the target prediction probability hypothesis density, target prediction label set, and target prediction Historical state matrix set;

所述新生目标的概率假设密度γk(x)的表达式为：The expression of the probability hypothesis density γ k (x) of the newborn target is:

Figure BDA00024654166300001318
Figure BDA00024654166300001318

式中，Jγ,k表示新生高斯分量的数目，

Figure BDA00024654166300001319
表示k时刻第j个新生高斯分量
Figure BDA00024654166300001320
的权值，
Figure BDA00024654166300001321
表示k时刻第j个新生高斯分量
Figure BDA00024654166300001322
的均值，
Figure BDA00024654166300001323
表示k时刻第j个新生高斯分量
Figure BDA00024654166300001324
的协方差矩阵；In the formula, J γ,k represents the number of newborn Gaussian components,
Figure BDA00024654166300001319
Indicates the jth newborn Gaussian component at time k
Figure BDA00024654166300001320
the weight of
Figure BDA00024654166300001321
Indicates the jth newborn Gaussian component at time k
Figure BDA00024654166300001322
the mean value of
Figure BDA00024654166300001323
Indicates the jth newborn Gaussian component at time k
Figure BDA00024654166300001324
The covariance matrix of ;

所述新生目标的标签集

Figure BDA0002465416630000141
的表达式为：The tag set for the nascent target
Figure BDA0002465416630000141
The expression is:

Figure BDA0002465416630000142
Figure BDA0002465416630000142

式中，

Figure BDA0002465416630000143
表示第j个新生高斯分量
Figure BDA0002465416630000144
的标签；In the formula,
Figure BDA0002465416630000143
Indicates the jth nascent Gaussian component
Figure BDA0002465416630000144
Tag of;

所述新生目标的历史状态矩阵集Λγ,k的表达式为：The historical state matrix set Λ γ of the newborn target, the expression of k is:

Figure BDA0002465416630000145
Figure BDA0002465416630000145

式中，

Figure BDA0002465416630000146
表示第j个新生高斯分量
Figure BDA0002465416630000147
的历史状态矩阵，且
Figure BDA0002465416630000148
In the formula,
Figure BDA0002465416630000146
Indicates the jth nascent Gaussian component
Figure BDA0002465416630000147
The historical state matrix of , and
Figure BDA0002465416630000148

所述存活目标的预测概率假设密度

Figure BDA0002465416630000149
的表达式为：The predicted probability hypothesis density for the survival target
Figure BDA0002465416630000149
The expression is:

Figure BDA00024654166300001410
Figure BDA00024654166300001410

式中，

Figure BDA00024654166300001411
表示第i个存活高斯分量
Figure BDA00024654166300001412
的预测权值，
Figure BDA00024654166300001413
表示第i个存活高斯分量
Figure BDA00024654166300001414
的预测均值，
Figure BDA00024654166300001415
表示第i个存活高斯分量
Figure BDA00024654166300001416
的预测协方差矩阵，Js,k|k-1表示在k时刻用k-1时刻高斯分量数目Jk-1所预测的存活高斯分量的预测数目；In the formula,
Figure BDA00024654166300001411
Denotes the i-th surviving Gaussian component
Figure BDA00024654166300001412
the predictive weight of
Figure BDA00024654166300001413
Denotes the i-th surviving Gaussian component
Figure BDA00024654166300001414
the predicted mean of
Figure BDA00024654166300001415
Denotes the i-th surviving Gaussian component
Figure BDA00024654166300001416
The prediction covariance matrix of , J s,k|k-1 represents the predicted number of surviving Gaussian components predicted by the number of Gaussian components J k - 1 at time k-1 at time k;

所述存活高斯分量

Figure BDA00024654166300001417
的预测权值
Figure BDA00024654166300001418
的表达式为：The survival Gaussian component
Figure BDA00024654166300001417
The prediction weight of
Figure BDA00024654166300001418
The expression is:

Figure BDA00024654166300001419
Figure BDA00024654166300001419

式中，ps表示存活概率，

Figure BDA00024654166300001420
表示k-1时刻第i个高斯分量
Figure BDA00024654166300001421
的权值；In the formula, p s represents the survival probability,
Figure BDA00024654166300001420
Represents the i-th Gaussian component at time k-1
Figure BDA00024654166300001421
the weight of

所述存活高斯分量

Figure BDA00024654166300001422
的预测均值
Figure BDA00024654166300001423
的表达式为：The survival Gaussian component
Figure BDA00024654166300001422
The predicted mean of
Figure BDA00024654166300001423
The expression is:

Figure BDA00024654166300001424
Figure BDA00024654166300001424

式中，Fk-1表示k-1时刻状态转移矩阵，

Figure BDA00024654166300001425
表示k-1时刻第i个高斯分量
Figure BDA00024654166300001426
的均值；In the formula, F k-1 represents the state transition matrix at time k-1,
Figure BDA00024654166300001425
Represents the i-th Gaussian component at time k-1
Figure BDA00024654166300001426
the mean value of

所述存活高斯分量

Figure BDA00024654166300001427
的预测协方差矩阵
Figure BDA00024654166300001428
的表达式为：The survival Gaussian component
Figure BDA00024654166300001427
The prediction covariance matrix of
Figure BDA00024654166300001428
The expression is:

Figure BDA00024654166300001429
Figure BDA00024654166300001429

式中，Qk-1表示k-1时刻过程噪声协方差矩阵，

Figure BDA00024654166300001430
表示k-1时刻第i个高斯分量
Figure BDA00024654166300001431
的协方差矩阵；In the formula, Q k-1 represents the process noise covariance matrix at time k-1,
Figure BDA00024654166300001430
Represents the i-th Gaussian component at time k-1
Figure BDA00024654166300001431
The covariance matrix of ;

所述存活高斯分量的预测数目Js,k|k-1的表达式为：The expression of the predicted number J s,k|k-1 of the survival Gaussian component is:

Js,k|k-1＝Jk-1；J s,k|k-1 = J k-1 ;

式中，Jk-1表示k-1时刻高斯分量的数目；In the formula, J k-1 represents the number of Gaussian components at time k-1;

所述存活目标的预测标签集

Figure BDA00024654166300001432
的表达式为：The predicted label set of the surviving target
Figure BDA00024654166300001432
The expression is:

Figure BDA0002465416630000151
Figure BDA0002465416630000151

式中，

Figure BDA0002465416630000152
表示k时刻第i个存活高斯分量
Figure BDA0002465416630000153
的预测标签，
Figure BDA0002465416630000154
表示k-1时刻第i个高斯分量
Figure BDA0002465416630000155
的标签；In the formula,
Figure BDA0002465416630000152
Indicates the i-th surviving Gaussian component at time k
Figure BDA0002465416630000153
the predicted label of
Figure BDA0002465416630000154
Represents the i-th Gaussian component at time k-1
Figure BDA0002465416630000155
Tag of;

所述存活目标的预测历史状态矩阵集Λs,k|k-1的表达式为：The expression of the predicted historical state matrix set Λ s,k|k-1 of the surviving target is:

Figure BDA0002465416630000156
Figure BDA0002465416630000156

式中，

Figure BDA0002465416630000157
表示k时刻第i个存活高斯分量
Figure BDA0002465416630000158
的预测历史状态矩阵；
Figure BDA0002465416630000159
Figure BDA00024654166300001510
表示k-1时刻第i个高斯分量
Figure BDA00024654166300001511
的历史状态矩阵
Figure BDA00024654166300001512
的第2列向量，
Figure BDA00024654166300001513
表示k-1时刻第i个高斯分量
Figure BDA00024654166300001514
的历史状态矩阵
Figure BDA00024654166300001515
的第δ列向量；In the formula,
Figure BDA0002465416630000157
Indicates the i-th surviving Gaussian component at time k
Figure BDA0002465416630000158
The predicted historical state matrix of ;
Figure BDA0002465416630000159
Figure BDA00024654166300001510
Represents the i-th Gaussian component at time k-1
Figure BDA00024654166300001511
The historical state matrix of
Figure BDA00024654166300001512
The 2nd column vector of ,
Figure BDA00024654166300001513
Represents the i-th Gaussian component at time k-1
Figure BDA00024654166300001514
The historical state matrix of
Figure BDA00024654166300001515
The δth column vector of ;

所述目标预测概率假设密度

Figure BDA00024654166300001516
的表达式为：The target predicted probability hypothesis density
Figure BDA00024654166300001516
The expression is:

Figure BDA00024654166300001517
Figure BDA00024654166300001517

式中，Jk|k-1表示预测高斯分量的预测数目，

Figure BDA00024654166300001518
表示第i个预测高斯分量
Figure BDA00024654166300001519
的预测权值，
Figure BDA00024654166300001520
表示第i个预测高斯分量
Figure BDA00024654166300001521
的预测均值，
Figure BDA00024654166300001522
表示第i个预测高斯分量
Figure BDA00024654166300001523
的预测协方差矩阵；In the formula, J k|k-1 represents the predicted number of predicted Gaussian components,
Figure BDA00024654166300001518
Indicates the i-th predicted Gaussian component
Figure BDA00024654166300001519
the predictive weight of
Figure BDA00024654166300001520
Indicates the i-th predicted Gaussian component
Figure BDA00024654166300001521
the predicted mean of
Figure BDA00024654166300001522
Indicates the i-th predicted Gaussian component
Figure BDA00024654166300001523
The prediction covariance matrix of ;

所述预测高斯分量的预测数目Jk|k-1的表达式为：The expression of the prediction number J k|k-1 of the predicted Gaussian component is:

Jk|k-1＝Js,k|k-1+Jγ,k；J k|k-1 = J s,k|k-1 +J γ,k ;

所述预测高斯分量

Figure BDA00024654166300001524
的预测权值
Figure BDA00024654166300001525
的表达式为：The predicted Gaussian component
Figure BDA00024654166300001524
The prediction weight of
Figure BDA00024654166300001525
The expression is:

Figure BDA00024654166300001526
Figure BDA00024654166300001526

式中，

Figure BDA00024654166300001527
表示k时刻用k-1时刻第i个高斯分量
Figure BDA00024654166300001528
的权值所预测的存活高斯分量
Figure BDA00024654166300001529
的预测权值；In the formula,
Figure BDA00024654166300001527
Indicates that k time uses the i-th Gaussian component at k-1 time
Figure BDA00024654166300001528
The survival Gaussian components predicted by the weights of
Figure BDA00024654166300001529
the predictive weight of

所述预测高斯分量

Figure BDA00024654166300001530
的预测均值
Figure BDA00024654166300001531
的表达式为：The predicted Gaussian component
Figure BDA00024654166300001530
The predicted mean of
Figure BDA00024654166300001531
The expression is:

Figure BDA00024654166300001532
Figure BDA00024654166300001532

式中，

Figure BDA0002465416630000161
表示k时刻用k-1时刻第i个高斯分量
Figure BDA0002465416630000162
的均值所预测的存活高斯分量
Figure BDA0002465416630000163
的预测均值；In the formula,
Figure BDA0002465416630000161
Indicates that k time uses the i-th Gaussian component at k-1 time
Figure BDA0002465416630000162
Gaussian component of survival predicted by the mean of
Figure BDA0002465416630000163
The predicted mean value of ;

所述预测高斯分量

Figure BDA0002465416630000164
的预测协方差矩阵
Figure BDA0002465416630000165
的表达式为：The predicted Gaussian component
Figure BDA0002465416630000164
The prediction covariance matrix of
Figure BDA0002465416630000165
The expression is:

Figure BDA0002465416630000166
Figure BDA0002465416630000166

式中，

Figure BDA0002465416630000167
表示k时刻用k-1时刻第i个高斯分量
Figure BDA0002465416630000168
的协方差矩阵所预测的存活高斯分量
Figure BDA0002465416630000169
的预测协方差矩阵；In the formula,
Figure BDA0002465416630000167
Indicates that k time uses the i-th Gaussian component at k-1 time
Figure BDA0002465416630000168
The survival Gaussian component predicted by the covariance matrix of
Figure BDA0002465416630000169
The prediction covariance matrix of ;

所述目标预测标签集

Figure BDA00024654166300001610
的表达式为：The target prediction label set
Figure BDA00024654166300001610
The expression is:

Figure BDA00024654166300001611
Figure BDA00024654166300001611

式中，

Figure BDA00024654166300001612
表示第i个预测高斯分量
Figure BDA00024654166300001613
的预测标签；In the formula,
Figure BDA00024654166300001612
Indicates the i-th predicted Gaussian component
Figure BDA00024654166300001613
the predicted label;

所述预测标签

Figure BDA00024654166300001614
的表达式为：The predicted label
Figure BDA00024654166300001614
The expression is:

Figure BDA00024654166300001615
Figure BDA00024654166300001615

所述目标预测历史状态矩阵集Λk|k-1的表达式为：The expression of the target prediction historical state matrix set Λ k|k-1 is:

Figure BDA00024654166300001616
Figure BDA00024654166300001616

式中，

Figure BDA00024654166300001617
表示第i个预测高斯分量
Figure BDA00024654166300001618
的预测历史状态矩阵；In the formula,
Figure BDA00024654166300001617
Indicates the i-th predicted Gaussian component
Figure BDA00024654166300001618
The predicted historical state matrix of ;

所述预测历史状态矩阵

Figure BDA00024654166300001619
的表达式为：The predicted history state matrix
Figure BDA00024654166300001619
The expression is:

Figure BDA00024654166300001620
Figure BDA00024654166300001620

步骤S3通过对前一时刻目标的概率假设密度、标签集和历史状态矩阵集进行一步预测，以得到当前时刻存活目标的预测概率假设密度、预测标签集和预测历史状态矩阵集，结合当前时刻新生目标的概率假设密度、标签集和历史状态矩阵集，以构建当前时刻所有目标的预测概率假设密度、预测标签集和预测历史状态矩阵集，为后续的目标更新做好准备工作。In step S3, one-step prediction is performed on the probability hypothesis density, label set and historical state matrix set of the target at the previous moment to obtain the predicted probability hypothesis density, predicted label set and predicted historical state matrix set of the surviving target at the current moment. The probability hypothesis density, label set and historical state matrix set of the target are used to construct the predicted probability hypothesis density, predicted label set and predicted historical state matrix set of all targets at the current moment, so as to prepare for the subsequent target update.

S4，基于量测集计算目标后验概率假设密度

Figure BDA00024654166300001621
目标后验标签集
Figure BDA00024654166300001622
和目标后验历史状态矩阵集Λk，重分配目标后验概率假设密度
Figure BDA00024654166300001623
中各高斯分量的权值；S4, calculate the target posterior probability hypothesis density based on the measurement set
Figure BDA00024654166300001621
target posterior label set
Figure BDA00024654166300001622
and the target posterior historical state matrix set Λ k , redistribute the target posterior probability hypothesis density
Figure BDA00024654166300001623
The weight of each Gaussian component in

所述量测集Zk的表达式为：The expression of the measurement set Z k is:

Figure BDA0002465416630000171
Figure BDA0002465416630000171

式中，Mk表示k时刻量测集Zk中量测的数目，

Figure BDA0002465416630000172
表示量测集Zk中的第j个量测；In the formula, M k represents the number of measurements in the measurement set Z k at time k,
Figure BDA0002465416630000172
Indicates the jth measurement in the measurement set Z k ;

所述计算目标后验概率假设密度

Figure BDA0002465416630000173
目标后验标签集
Figure BDA0002465416630000174
和目标后验历史状态矩阵集Λk，包括如下步骤：The computed target posterior probability hypothesis density
Figure BDA0002465416630000173
target posterior label set
Figure BDA0002465416630000174
and the target posterior historical state matrix set Λ k , including the following steps:

S4.1：计算目标的高斯分量

Figure BDA0002465416630000175
的权值
Figure BDA0002465416630000176
均值
Figure BDA0002465416630000177
协方差矩阵
Figure BDA0002465416630000178
标签
Figure BDA0002465416630000179
历史状态矩阵
Figure BDA00024654166300001710
S4.1: Calculate the Gaussian components of the target
Figure BDA0002465416630000175
weight of
Figure BDA0002465416630000176
average
Figure BDA0002465416630000177
covariance matrix
Figure BDA0002465416630000178
Label
Figure BDA0002465416630000179
Historical State Matrix
Figure BDA00024654166300001710

所述高斯分量

Figure BDA00024654166300001711
的权值
Figure BDA00024654166300001712
的表达式为：The Gaussian component
Figure BDA00024654166300001711
weight of
Figure BDA00024654166300001712
The expression is:

Figure BDA00024654166300001713
Figure BDA00024654166300001713

式中，

Figure BDA00024654166300001714
表示基于量测
Figure BDA00024654166300001715
的杂波强度，pd表示检测概率，Hk表示k时刻量测矩阵；Rk表示k时刻量测噪声协方差矩阵，
Figure BDA00024654166300001716
表示预测高斯分量
Figure BDA00024654166300001717
的预测权值，
Figure BDA00024654166300001718
表示预测高斯分量
Figure BDA00024654166300001719
的预测均值，
Figure BDA00024654166300001720
表示预测高斯分量
Figure BDA00024654166300001721
的预测协方差矩阵；In the formula,
Figure BDA00024654166300001714
Indicates based on measurement
Figure BDA00024654166300001715
clutter intensity, p d represents the detection probability, H k represents the measurement matrix at time k; R k represents the measurement noise covariance matrix at time k,
Figure BDA00024654166300001716
represents the predicted Gaussian component
Figure BDA00024654166300001717
the predictive weight of
Figure BDA00024654166300001718
represents the predicted Gaussian component
Figure BDA00024654166300001719
the predicted mean of
Figure BDA00024654166300001720
represents the predicted Gaussian component
Figure BDA00024654166300001721
The prediction covariance matrix of ;

所述高斯分量

Figure BDA00024654166300001722
的均值
Figure BDA00024654166300001723
的表达式为：The Gaussian component
Figure BDA00024654166300001722
mean of
Figure BDA00024654166300001723
The expression is:

Figure BDA00024654166300001724
Figure BDA00024654166300001724

式中，

Figure BDA00024654166300001725
表示高斯分量
Figure BDA00024654166300001726
的信息增益，且
Figure BDA00024654166300001727
In the formula,
Figure BDA00024654166300001725
Represents the Gaussian component
Figure BDA00024654166300001726
information gain, and
Figure BDA00024654166300001727

所述高斯分量

Figure BDA00024654166300001728
的协方差矩阵
Figure BDA00024654166300001729
的表达式为：The Gaussian component
Figure BDA00024654166300001728
The covariance matrix of
Figure BDA00024654166300001729
The expression is:

Figure BDA00024654166300001730
Figure BDA00024654166300001730

式中，I表示单位矩阵；In the formula, I represents the identity matrix;

所述高斯分量

Figure BDA00024654166300001731
的标签
Figure BDA00024654166300001732
的表达式为：The Gaussian component
Figure BDA00024654166300001731
Tag of
Figure BDA00024654166300001732
The expression is:

Figure BDA00024654166300001733
Figure BDA00024654166300001733

所述高斯分量

Figure BDA00024654166300001734
的历史状态矩阵
Figure BDA00024654166300001735
的表达式为：The Gaussian component
Figure BDA00024654166300001734
The historical state matrix of
Figure BDA00024654166300001735
The expression is:

Figure BDA00024654166300001736
Figure BDA00024654166300001736

式中，

Figure BDA00024654166300001737
表示预测高斯分量
Figure BDA00024654166300001738
的预测历史状态矩阵
Figure BDA00024654166300001739
的第1列向量，
Figure BDA00024654166300001740
表示预测高斯分量
Figure BDA00024654166300001741
的预测历史状态矩阵
Figure BDA00024654166300001742
的第δ-1列向量，
Figure BDA00024654166300001743
表示高斯分量
Figure BDA00024654166300001744
的均值；In the formula,
Figure BDA00024654166300001737
represents the predicted Gaussian component
Figure BDA00024654166300001738
The forecast history state matrix of
Figure BDA00024654166300001739
The first column vector of ,
Figure BDA00024654166300001740
represents the predicted Gaussian component
Figure BDA00024654166300001741
The forecast history state matrix of
Figure BDA00024654166300001742
The δ-1th column vector of ,
Figure BDA00024654166300001743
Represents the Gaussian component
Figure BDA00024654166300001744
the mean value of

S4.2，计算高斯分量

Figure BDA0002465416630000181
所对应的非归一化权值矩阵Ak和归一化权值矩阵Bk，以对各高斯分量的权值进行再分配，并输出目标后验概率假设密度
Figure BDA0002465416630000182
目标后验标签集
Figure BDA0002465416630000183
和目标后验历史状态矩阵集Λk；S4.2, Calculation of Gaussian components
Figure BDA0002465416630000181
The corresponding unnormalized weight matrix A k and normalized weight matrix B k are used to redistribute the weights of each Gaussian component, and output the target posterior probability hypothesis density
Figure BDA0002465416630000182
target posterior label set
Figure BDA0002465416630000183
and the target posterior history state matrix set Λ k ;

所述非归一化权值矩阵Ak的表达式为：The expression of the non-normalized weight matrix A k is:

Figure BDA0002465416630000184
Figure BDA0002465416630000184

式中，

Figure BDA0002465416630000185
表示高斯分量
Figure BDA0002465416630000186
的非归一化权值，且
Figure BDA0002465416630000187
In the formula,
Figure BDA0002465416630000185
Represents the Gaussian component
Figure BDA0002465416630000186
The unnormalized weights of , and
Figure BDA0002465416630000187

归一化权值矩阵Bk的表达式为：The expression of the normalized weight matrix B k is:

Figure BDA0002465416630000188
Figure BDA0002465416630000188

式中，

Figure BDA0002465416630000189
表示高斯分量
Figure BDA00024654166300001810
的权值。In the formula,
Figure BDA0002465416630000189
Represents the Gaussian component
Figure BDA00024654166300001810
weights.

然后，设定高斯分量索引集

Figure BDA00024654166300001811
一个初始值为空的优化权值矩阵Ek，之后对各高斯分量的权值进行再分配；Then, set the Gaussian component index set
Figure BDA00024654166300001811
An optimized weight matrix E k whose initial value is empty, and then redistribute the weights of each Gaussian component;

所述对各高斯分量的权值再分配，并输出目标后验概率假设密度

Figure BDA00024654166300001812
目标后验标签集
Figure BDA00024654166300001813
和目标后验历史状态矩阵集Λk包括如下步骤：The weight redistribution of each Gaussian component, and output the target posterior probability hypothesis density
Figure BDA00024654166300001812
target posterior label set
Figure BDA00024654166300001813
and the target posterior historical state matrix set Λ k include the following steps:

S4.2.1，查找归一化权值矩阵Bk中的最大权值的索引<i*,j*>，构建与该最大权值高斯分量具有相同标签的分量索引集Ψ，计算分量索引集Ψ中索引所对应的高斯分量的权值和ηw；S4.2.1, find the index <i * , j * > of the maximum weight in the normalized weight matrix B k , construct a component index set Ψ with the same label as the maximum weight Gaussian component, and calculate the component index set Ψ The weight sum η w of the Gaussian component corresponding to the index in ;

所述最大权值的索引<i*,j*>的表达式为：The expression of the index <i * , j * > of the maximum weight is:

Figure BDA00024654166300001814
Figure BDA00024654166300001814

式中，Mk表示量测集Zk中量测的数目；In the formula, M k represents the number of measurements in the measurement set Z k ;

所述分量索引集Ψ的表达式为：The expression of the component index set Ψ is:

Figure BDA00024654166300001815
Figure BDA00024654166300001815

式中，

Figure BDA00024654166300001816
表示高斯分量
Figure BDA00024654166300001817
的标签，
Figure BDA00024654166300001818
表示高斯分量
Figure BDA00024654166300001819
的标签；In the formula,
Figure BDA00024654166300001816
Represents the Gaussian component
Figure BDA00024654166300001817
Tag of,
Figure BDA00024654166300001818
Represents the Gaussian component
Figure BDA00024654166300001819
Tag of;

所述权值和ηw的表达式为：The expression of described weight and η w is:

Figure BDA0002465416630000191
Figure BDA0002465416630000191

S4.2.2，计算标志位

Figure BDA0002465416630000192
如果标志位
Figure BDA0002465416630000193
则更新分量索引集Ψ中索引所对应的高斯分量的权值和ηw和标志位
Figure BDA0002465416630000194
若标志位
Figure BDA0002465416630000195
则执行步骤S4.2.3；S4.2.2, Calculation flag bit
Figure BDA0002465416630000192
if flag
Figure BDA0002465416630000193
Then update the weight and η w and the flag bit of the Gaussian component corresponding to the index in the component index set Ψ
Figure BDA0002465416630000194
If flag
Figure BDA0002465416630000195
Then execute step S4.2.3;

所述标志位

Figure BDA0002465416630000196
的表达式为：The flag bit
Figure BDA0002465416630000196
The expression is:

Figure BDA0002465416630000197
Figure BDA0002465416630000197

所述更新分量索引集中索引所对应的高斯分量的权值和ηw和标志位

Figure BDA0002465416630000198
包括如下步骤：The weight sum η w and the flag bit of the Gaussian component corresponding to the index in the update component index set
Figure BDA0002465416630000198
Including the following steps:

S4.2.2a，从具有相同标签

Figure BDA0002465416630000199
的高斯分量中选择具有最小加权Hungarian距离的高斯分量；S4.2.2a, from the same label
Figure BDA0002465416630000199
Select the Gaussian component with the smallest weighted Hungarian distance among the Gaussian components of ;

所述高斯分量所对应的索引<ir,jc>的表达式为：The expression of the index <i r , j c > corresponding to the Gaussian component is:

Figure BDA00024654166300001910
Figure BDA00024654166300001910

其中，

Figure BDA00024654166300001911
in,
Figure BDA00024654166300001911

式中，比例系数ζ＝[1,δ-1/δ,δ-2/δ,δ-3/δ,δ-4/δ]，

Figure BDA00024654166300001912
表示高斯分量
Figure BDA00024654166300001913
在k时刻的历史状态矩阵
Figure BDA00024654166300001914
的第l列向量，
Figure BDA00024654166300001915
表示
Figure BDA00024654166300001916
与量测
Figure BDA00024654166300001917
间的Hungarian距离，其中，
Figure BDA00024654166300001918
In the formula, the proportional coefficient ζ=[1, δ-1/δ, δ-2/δ, δ-3/δ, δ-4/δ],
Figure BDA00024654166300001912
Represents the Gaussian component
Figure BDA00024654166300001913
Historical state matrix at time k
Figure BDA00024654166300001914
The l-th column of the vector,
Figure BDA00024654166300001915
express
Figure BDA00024654166300001916
and measurement
Figure BDA00024654166300001917
The Hungarian distance between, where,
Figure BDA00024654166300001918

S4.2.2b，更新非归一化权值矩阵Ak和归一化权值矩阵Bk中的各权值，对应的表达式分别为：S4.2.2b, update the weights in the unnormalized weight matrix A k and the normalized weight matrix B k , the corresponding expressions are respectively:

Figure BDA00024654166300001919
Figure BDA00024654166300001919

式中，比例因子

Figure BDA00024654166300001920
Figure BDA00024654166300001921
表示高斯分量
Figure BDA00024654166300001922
的标签；In the formula, the scale factor
Figure BDA00024654166300001920
Figure BDA00024654166300001921
Represents the Gaussian component
Figure BDA00024654166300001922
Tag of;

Figure BDA00024654166300001923
Figure BDA00024654166300001923

S4.2.2c，更新分量索引集Ψ中索引所对应的高斯分量的权值和ηw和标志位

Figure BDA00024654166300001924
如果标志位
Figure BDA00024654166300001925
则返回执行步骤S4.2.2b，若标志位
Figure BDA00024654166300001926
则执行步骤S4.2.3；S4.2.2c, update the weight and η w and flag bit of the Gaussian component corresponding to the index in the component index set Ψ
Figure BDA00024654166300001924
if flag
Figure BDA00024654166300001925
Then return to step S4.2.2b, if the flag
Figure BDA00024654166300001926
Then execute step S4.2.3;

S4.2.3，将归一化权值矩阵Bk中的权值

Figure BDA00024654166300001927
拷贝到优化权值矩阵Ek中的对应位置，其中，i∈Ψ、j＝1:Mk；S4.2.3, normalize the weights in the weight matrix B k
Figure BDA00024654166300001927
Copy to the corresponding position in the optimization weight matrix E k , wherein, i∈Ψ, j=1:M k ;

S4.2.4，更新高斯分量索引集

Figure BDA0002465416630000201
如果高斯分量索引集
Figure BDA0002465416630000202
为空，则继续执行步骤S4.2.5，否则返回执行步骤S4.2.1；S4.2.4, update Gaussian component index set
Figure BDA0002465416630000201
If the Gaussian component index set
Figure BDA0002465416630000202
If it is empty, continue to execute step S4.2.5, otherwise return to execute step S4.2.1;

所述更新高斯分量索引集

Figure BDA0002465416630000203
的表达式为：The updated Gaussian component index set
Figure BDA0002465416630000203
The expression is:

Figure BDA0002465416630000204
Figure BDA0002465416630000204

S4.2.5，基于优化权值矩阵Ek中的权值，更新目标后验概率假设密度

Figure BDA0002465416630000205
中的相应高斯分量的权值；输出目标后验概率假设密度
Figure BDA0002465416630000206
目标后验标签集
Figure BDA0002465416630000207
和目标后验历史状态矩阵集Λk；S4.2.5, update the target posterior probability hypothesis density based on the weights in the optimized weight matrix E k
Figure BDA0002465416630000205
The weights of the corresponding Gaussian components in ; the output target posterior probability hypothesis density
Figure BDA0002465416630000206
target posterior label set
Figure BDA0002465416630000207
and the target posterior history state matrix set Λ k ;

所述目标后验概率假设密度

Figure BDA0002465416630000208
的表达式为：The target posterior probability hypothesis density
Figure BDA0002465416630000208
The expression is:

Figure BDA0002465416630000209
Figure BDA0002465416630000209

所述目标后验标签集

Figure BDA00024654166300002010
的表达式为：The target posterior label set
Figure BDA00024654166300002010
The expression is:

Figure BDA00024654166300002011
Figure BDA00024654166300002011

所述目标后验历史状态矩阵集Λk的表达式为：The expression of the target posterior history state matrix set Λ k is:

Figure BDA00024654166300002012
Figure BDA00024654166300002012

步骤S4.2通过对高斯分量的权值进行再分配，得到了高精度的目标后验概率假设密度。In step S4.2, the high-precision target posterior probability hypothesis density is obtained by redistributing the weights of the Gaussian components.

S5，对步骤S4中所获得的高斯分量集

Figure BDA00024654166300002013
及其参数集进行变换，并对变换后的高斯分量集进行约简；S5, for the Gaussian component set obtained in step S4
Figure BDA00024654166300002013
and its parameter set are transformed, and the transformed Gaussian component set is reduced;

所述高斯分量集

Figure BDA00024654166300002014
所对应的参数集为
Figure BDA00024654166300002015
且变换后的高斯分量集及其参数集分别为
Figure BDA00024654166300002016
和
Figure BDA00024654166300002017
其中分量数目为Jk＝Jk|k-1+Jk|k-1×Mk；The set of Gaussian components
Figure BDA00024654166300002014
The corresponding parameter set is
Figure BDA00024654166300002015
And the transformed Gaussian component set and its parameter set are respectively
Figure BDA00024654166300002016
and
Figure BDA00024654166300002017
The number of components is J k ＝J k|k-1 +J k|k-1 ×M k ;

变换后的高斯分量

Figure BDA00024654166300002018
的表达式为：Transformed Gaussian components
Figure BDA00024654166300002018
The expression is:

Figure BDA00024654166300002019
Figure BDA00024654166300002019

变换后的高斯分量

Figure BDA00024654166300002020
的权值
Figure BDA00024654166300002021
表达式为：Transformed Gaussian components
Figure BDA00024654166300002020
weight of
Figure BDA00024654166300002021
The expression is:

Figure BDA00024654166300002022
Figure BDA00024654166300002022

变换后的高斯分量

Figure BDA00024654166300002023
的均值
Figure BDA00024654166300002024
表达式为：Transformed Gaussian components
Figure BDA00024654166300002023
mean of
Figure BDA00024654166300002024
The expression is:

Figure BDA0002465416630000211
Figure BDA0002465416630000211

变换后的高斯分量

Figure BDA0002465416630000212
的协方差矩阵
Figure BDA0002465416630000213
表达式为：Transformed Gaussian components
Figure BDA0002465416630000212
The covariance matrix of
Figure BDA0002465416630000213
The expression is:

Figure BDA0002465416630000214
Figure BDA0002465416630000214

变换后的高斯分量

Figure BDA0002465416630000215
的标签
Figure BDA0002465416630000216
表达式为：Transformed Gaussian components
Figure BDA0002465416630000215
Tag of
Figure BDA0002465416630000216
The expression is:

Figure BDA0002465416630000217
Figure BDA0002465416630000217

变换后的高斯分量

Figure BDA0002465416630000218
的历史状态矩阵
Figure BDA0002465416630000219
表达式为：Transformed Gaussian components
Figure BDA0002465416630000218
The historical state matrix of
Figure BDA0002465416630000219
The expression is:

Figure BDA00024654166300002110
Figure BDA00024654166300002110

所述对变换后的高斯分量集进行约简包括步骤如下：The step of reducing the transformed Gaussian component set includes the following steps:

S5.1，设定删减阈值T1，融合阈值U，最大高斯分量数目阈值Jmax。S5.1, setting the pruning threshold T 1 , the fusion threshold U, and the maximum Gaussian component number threshold J max .

S5.2，设定计数变量j＝0和高斯分量数目变量

Figure BDA00024654166300002111
高斯分量索引集
Figure BDA00024654166300002112
S5.2, set count variable j=0 and Gaussian component number variable
Figure BDA00024654166300002111
Gaussian component index set
Figure BDA00024654166300002112

式中，

Figure BDA00024654166300002113
表示高斯分量
Figure BDA00024654166300002114
的权值。In the formula,
Figure BDA00024654166300002113
Represents the Gaussian component
Figure BDA00024654166300002114
weights.

S5.3，执行j＝j+1，筛选具有最大权值的高斯分量

Figure BDA00024654166300002115
以建立新的高斯分量；S5.3, execute j=j+1, and filter the Gaussian component with the largest weight
Figure BDA00024654166300002115
to create a new Gaussian component;

所述最大权值的高斯分量

Figure BDA00024654166300002116
的索引l*的表达式为：the Gaussian component of the maximum weight
Figure BDA00024654166300002116
The expression for the index l * is:

Figure BDA00024654166300002117
Figure BDA00024654166300002117

所述建立新的高斯分量包括如下步骤：The establishment of a new Gaussian component includes the following steps:

S5.3.1，定义第一过渡索引集L1；S5.3.1, define the first transition index set L1;

所述第一过渡索引集L1的表达式为：The expression of the first transition index set L1 is:

Figure BDA00024654166300002118
Figure BDA00024654166300002118

式中，

Figure BDA00024654166300002119
表示最大权值的高斯分量
Figure BDA00024654166300002120
的标签，
Figure BDA00024654166300002121
表示高斯分量
Figure BDA00024654166300002122
的标签；In the formula,
Figure BDA00024654166300002119
Gaussian component representing the maximum weight
Figure BDA00024654166300002120
Tag of,
Figure BDA00024654166300002121
Represents the Gaussian component
Figure BDA00024654166300002122
Tag of;

S5.3.2，定义第二过渡索引集L2；S5.3.2, define the second transition index set L2;

所述第二过渡索引集L2的表达式为：The expression of the second transition index set L2 is:

Figure BDA00024654166300002123
Figure BDA00024654166300002123

式中，

Figure BDA00024654166300002124
表示最大权值的高斯分量
Figure BDA00024654166300002125
的均值，
Figure BDA00024654166300002126
表示最大权值的高斯分量
Figure BDA00024654166300002127
的协方差矩阵，
Figure BDA0002465416630000221
表示高斯分量
Figure BDA0002465416630000222
的均值；In the formula,
Figure BDA00024654166300002124
Gaussian component representing the maximum weight
Figure BDA00024654166300002125
the mean value of
Figure BDA00024654166300002126
Gaussian component representing the maximum weight
Figure BDA00024654166300002127
The covariance matrix of ,
Figure BDA0002465416630000221
Represents the Gaussian component
Figure BDA0002465416630000222
the mean value of

S5.3.3，将第二过渡索引集L2中索引所对应的高斯分量

Figure BDA0002465416630000223
合并为一个新的高斯分量
Figure BDA0002465416630000224
S5.3.3, the Gaussian component corresponding to the index in the second transition index set L2
Figure BDA0002465416630000223
combined into a new Gaussian component
Figure BDA0002465416630000224

所述新的高斯分量

Figure BDA0002465416630000225
的权值
Figure BDA0002465416630000226
的表达式为：The new Gaussian component
Figure BDA0002465416630000225
weight of
Figure BDA0002465416630000226
The expression is:

Figure BDA0002465416630000227
Figure BDA0002465416630000227

式中，

Figure BDA0002465416630000228
表示高斯分量
Figure BDA0002465416630000229
的权值；In the formula,
Figure BDA0002465416630000228
Represents the Gaussian component
Figure BDA0002465416630000229
the weight of

所述新的高斯分量

Figure BDA00024654166300002210
的均值
Figure BDA00024654166300002211
的表达式为：The new Gaussian component
Figure BDA00024654166300002210
mean of
Figure BDA00024654166300002211
The expression is:

Figure BDA00024654166300002212
Figure BDA00024654166300002212

所述新的高斯分量

Figure BDA00024654166300002213
的协方差矩阵
Figure BDA00024654166300002214
的表达式为：The new Gaussian component
Figure BDA00024654166300002213
The covariance matrix of
Figure BDA00024654166300002214
The expression is:

Figure BDA00024654166300002215
Figure BDA00024654166300002215

式中，

Figure BDA00024654166300002216
表示最大权值的高斯分量
Figure BDA00024654166300002217
的均值，
Figure BDA00024654166300002218
表示高斯分量
Figure BDA00024654166300002219
的协方差矩阵；In the formula,
Figure BDA00024654166300002216
Gaussian component representing the maximum weight
Figure BDA00024654166300002217
the mean value of
Figure BDA00024654166300002218
Represents the Gaussian component
Figure BDA00024654166300002219
The covariance matrix of ;

所述新的高斯分量

Figure BDA00024654166300002220
的标签
Figure BDA00024654166300002221
的表达式为：The new Gaussian component
Figure BDA00024654166300002220
Tag of
Figure BDA00024654166300002221
The expression is:

Figure BDA00024654166300002222
Figure BDA00024654166300002222

所述新的高斯分量

Figure BDA00024654166300002223
的历史状态矩阵
Figure BDA00024654166300002224
的表达式为：The new Gaussian component
Figure BDA00024654166300002223
The historical state matrix of
Figure BDA00024654166300002224
The expression is:

Figure BDA00024654166300002225
Figure BDA00024654166300002225

式中，

Figure BDA00024654166300002226
表示最大权值的高斯分量
Figure BDA00024654166300002227
的历史状态矩阵
Figure BDA00024654166300002228
的第1列向量，
Figure BDA00024654166300002229
表示最大权值的高斯分量
Figure BDA00024654166300002230
的历史状态矩阵
Figure BDA00024654166300002231
的第δ-1列向量。In the formula,
Figure BDA00024654166300002226
Gaussian component representing the maximum weight
Figure BDA00024654166300002227
The historical state matrix of
Figure BDA00024654166300002228
The first column vector of ,
Figure BDA00024654166300002229
Gaussian component representing the maximum weight
Figure BDA00024654166300002230
The historical state matrix of
Figure BDA00024654166300002231
The δ-1th column vector of .

S5.4，更新高斯分量索引集

Figure BDA00024654166300002232
若高斯分量索引集
Figure BDA00024654166300002233
不为空，则返回执行步骤S5.3；若高斯分量索引集
Figure BDA00024654166300002234
为空，更新高斯分量数目变量
Figure BDA00024654166300002235
且执行步骤S5.5；S5.4, update Gaussian component index set
Figure BDA00024654166300002232
If the Gaussian component index set
Figure BDA00024654166300002233
is not empty, return to step S5.3; if Gaussian component index set
Figure BDA00024654166300002234
If it is empty, update the Gaussian component number variable
Figure BDA00024654166300002235
And execute step S5.5;

所述更新高斯分量索引集

Figure BDA00024654166300002236
的表达式为：The updated Gaussian component index set
Figure BDA00024654166300002236
The expression is:

Figure BDA00024654166300002237
Figure BDA00024654166300002237

所述更新高斯分量数目变量

Figure BDA00024654166300002238
的表达式为：The updated Gaussian component number variable
Figure BDA00024654166300002238
The expression is:

Figure BDA00024654166300002239
Figure BDA00024654166300002239

S5.5，对高斯分量数目变量

Figure BDA00024654166300002240
和最大高斯分量数目阈值Jmax的值进行比较，根据新的高斯分量集
Figure BDA00024654166300002241
获得约简后的高斯分量集
Figure BDA00024654166300002242
S5.5, for the number of Gaussian components variable
Figure BDA00024654166300002240
Compared with the value of the maximum Gaussian component number threshold J max , according to the new Gaussian component set
Figure BDA00024654166300002241
Obtain the reduced Gaussian component set
Figure BDA00024654166300002242

如果

Figure BDA00024654166300002243
按权值
Figure BDA00024654166300002244
由大到小的顺序对所获得的新的高斯分量集
Figure BDA00024654166300002245
进行排列，取前Jmax个高斯分量构建约简后的高斯分量集
Figure BDA0002465416630000231
其中
Figure BDA0002465416630000232
Jk＝Jmax；若
Figure BDA0002465416630000233
则新的高斯分量集
Figure BDA0002465416630000234
为约简后的高斯分量集
Figure BDA0002465416630000235
其中
Figure BDA0002465416630000236
if
Figure BDA00024654166300002243
by weight
Figure BDA00024654166300002244
The new set of Gaussian components obtained by ordering from large to small
Figure BDA00024654166300002245
Arrange and take the first J max Gaussian components to construct the reduced Gaussian component set
Figure BDA0002465416630000231
in
Figure BDA0002465416630000232
J k = J max ; if
Figure BDA0002465416630000233
Then the new set of Gaussian components
Figure BDA0002465416630000234
is the reduced Gaussian component set
Figure BDA0002465416630000235
in
Figure BDA0002465416630000236

所述约简后的高斯分量集

Figure BDA0002465416630000237
所对应的参数集为
Figure BDA0002465416630000238
The reduced Gaussian component set
Figure BDA0002465416630000237
The corresponding parameter set is
Figure BDA0002465416630000238

步骤S5通过对高斯分量进行约简，实现了对高斯分量的优化重组，降低了无效高斯分量的数目，能够有效地提高跟踪算法的计算效率。In step S5, Gaussian components are reduced to achieve optimal reorganization of Gaussian components, reducing the number of invalid Gaussian components, and effectively improving the calculation efficiency of the tracking algorithm.

S6，根据步骤S5中所获得的约简后的高斯分量集，估计目标的状态和数目，包括如下步骤：S6, according to the reduced Gaussian component set obtained in step S5, estimate the state and number of the target, including the following steps:

S6.1，根据约简后的高斯分量参数集

Figure BDA0002465416630000239
中的权值
Figure BDA00024654166300002310
估计目标数目Nk；S6.1, according to the reduced Gaussian component parameter set
Figure BDA0002465416630000239
weights in
Figure BDA00024654166300002310
Estimated target number N k ;

所述目标数目Nk的表达式为：The expression of the target number N k is:

Figure BDA00024654166300002311
Figure BDA00024654166300002311

S6.2，从高斯分量参数集

Figure BDA00024654166300002312
中选择权值
Figure BDA00024654166300002313
大于0.5的索引，并将这些索引所对应的高斯分量
Figure BDA00024654166300002314
作为真实目标，输出这些高斯分量
Figure BDA00024654166300002315
的均值
Figure BDA00024654166300002316
作为当前时刻的目标状态估计。S6.2, from the Gaussian component parameter set
Figure BDA00024654166300002312
choose the weight
Figure BDA00024654166300002313
Indexes greater than 0.5, and the Gaussian components corresponding to these indices
Figure BDA00024654166300002314
As real targets, output these Gaussian components
Figure BDA00024654166300002315
mean of
Figure BDA00024654166300002316
as the target state estimate at the current moment.

步骤S6实现了从当前时刻高斯分量参数集中估计目标的状态和数目。Step S6 realizes estimating the state and number of targets from the Gaussian component parameter set at the current moment.

S7，若跟踪单一时刻，则目标跟踪结束；若跟踪若干个时刻，则重复执行S3-S6直至迭代所有时刻。S7. If a single moment is tracked, the target tracking ends; if several moments are tracked, S3-S6 is repeatedly executed until all moments are iterated.

本发明的效果可通过以下仿真实验进一步说明：Effect of the present invention can be further illustrated by following simulation experiments:

①仿真条件及参数①Simulation conditions and parameters

图2是本发明试验采用的一个二维跟踪区域内目标真实轨迹及量测在100个时刻的仿真示意图，且杂波均值为5。k时刻的目标状态为

Figure BDA00024654166300002317
其中
Figure BDA00024654166300002318
为目标的位置，
Figure BDA00024654166300002319
为目标的速度。目标运动方程及量测方程分别如下：Fig. 2 is a simulation schematic diagram of the real trajectory and measurement of the target at 100 moments in a two-dimensional tracking area used in the experiment of the present invention, and the average value of the clutter is 5. The target state at time k is
Figure BDA00024654166300002317
in
Figure BDA00024654166300002318
for the target position,
Figure BDA00024654166300002319
for the target speed. The target motion equation and measurement equation are as follows:

xk＝Fk-1xk-1+Qk-1；x k = F k-1 x k-1 + Q k-1 ;

zk＝Hkxk+Rk；z k = H k x k + R k ;

其中，in,

Figure BDA00024654166300002320
Figure BDA00024654166300002320

Figure BDA0002465416630000241
Figure BDA0002465416630000241

Figure BDA0002465416630000242
Figure BDA0002465416630000242

Figure BDA0002465416630000243
Figure BDA0002465416630000243

仿真场景中，过程噪声σw为一个均值为0、标准差为0.5m的高斯白噪声，量测噪声σv为一个均值为0、标准差为50m的高斯白噪声，检测概率pd＝0.98，存活概率ps＝0.99。设置删减阈值T1＝10-5，融合阈值U＝4，最大高斯分量数目阈值Jmax＝100，元素数目阈值δ＝5。假设k＝0时刻初始化的目标概率假设密度为：In the simulation scenario, the process noise σ w is a Gaussian white noise with a mean value of 0 and a standard deviation of 0.5m, the measurement noise σv is a Gaussian white noise with a mean value of 0 and a standard deviation of 50m, and the detection probability p d =0.98 , survival probability p s =0.99. Set the pruning threshold T 1 =10 −5 , the fusion threshold U=4, the maximum Gaussian component number threshold J max =100, and the element number threshold δ=5. Assume that the target probability hypothesis density initialized at time k=0 is:

Figure BDA0002465416630000244
Figure BDA0002465416630000244

其中，

Figure BDA0002465416630000245
Figure BDA0002465416630000246
三个目标的标签分别为
Figure BDA0002465416630000247
和
Figure BDA0002465416630000248
三个目标的历史状态矩阵分别为
Figure BDA0002465416630000249
和
Figure BDA00024654166300002410
in,
Figure BDA0002465416630000245
Figure BDA0002465416630000246
The labels of the three targets are
Figure BDA0002465416630000247
and
Figure BDA0002465416630000248
The historical state matrices of the three targets are
Figure BDA0002465416630000249
and
Figure BDA00024654166300002410

②仿真结果与分析②Simulation results and analysis

仿真实验中，本发明MCST-GM-PHD分别与GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法进行多目标跟踪性能对比。本发明中采用OSPA距离和目标数目估计数为跟踪性能度量指标，其中OSPA距离的两个参数分别为c＝100和p＝2。OSPA距离越小，目标状态精度越高。每个实验结果均为200次蒙特卡罗仿真的均值。实验主要从以下三个方面开展：In the simulation experiment, the MCST-GM-PHD of the present invention is compared with the GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods for multi-target tracking performance. In the present invention, the OSPA distance and the estimated number of targets are used as the tracking performance index, and the two parameters of the OSPA distance are c=100 and p=2 respectively. The smaller the OSPA distance, the higher the target state accuracy. Each experimental result is the mean of 200 Monte Carlo simulations. The experiment is mainly carried out from the following three aspects:

实验1:杂波干扰下的多目标场景Experiment 1: Multi-target scene under clutter interference

图3是采用本发明MCST-GM-PHD与GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法的平均OSPA距离对比效果图。可以看出，本发明MCST-GM-PHD的目标状态估计精度优于GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法。Fig. 3 is a comparison effect diagram of the average OSPA distance using the MCST-GM-PHD method of the present invention and the GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods. It can be seen that the target state estimation accuracy of MCST-GM-PHD of the present invention is better than that of GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods.

图4是采用本发明MCST-GM-PHD与GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法的平均目标数目估计数对比效果图。可以看出，本发明MCST-GM-PHD的目标数目估计精度与IR-GM-PHD方法相当，且均能够准确地估计出目标数目；本发明MCST-GM-PHD的目标数目估计精度优于GM-PHD、P-GM-PHD和CP-GM-PHD方法。Fig. 4 is a comparison effect diagram of the average target number estimates using the MCST-GM-PHD method of the present invention and the GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods. It can be seen that the target number estimation accuracy of MCST-GM-PHD of the present invention is equivalent to the IR-GM-PHD method, and both can accurately estimate the target number; the target number estimation accuracy of MCST-GM-PHD of the present invention is better than GM - PHD, P-GM-PHD and CP-GM-PHD methods.

实验2:不同杂波均值下的多目标场景Experiment 2: Multi-target scene with different clutter means

图5是不同杂波均值环境下采用本发明MCST-GM-PHD与GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法的平均OSPA距离对比效果图。可以看出，在不同杂波均值环境下本发明MCST-GM-PHD的目标状态估计精度优于GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法。Fig. 5 is a comparison effect diagram of the average OSPA distance using the MCST-GM-PHD of the present invention and the GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods under different clutter mean environments. It can be seen that the target state estimation accuracy of MCST-GM-PHD of the present invention is better than that of GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods under different clutter mean environments.

图6是不同杂波均值环境下采用本发明MCST-GM-PHD与GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法的平均目标数目估计数对比效果图。可以看出，在不同杂波均值环境下本发明MCST-GM-PHD的目标数目估计精度与IR-GM-PHD方法相当，且优于GM-PHD、P-GM-PHD和CP-GM-PHD方法。Fig. 6 is a comparison effect diagram of the average target number estimates using the MCST-GM-PHD of the present invention and the GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods under different clutter mean environments. It can be seen that the target number estimation accuracy of the MCST-GM-PHD of the present invention is equivalent to that of the IR-GM-PHD method under different clutter mean environments, and is better than GM-PHD, P-GM-PHD and CP-GM-PHD method.

实验3:不同检测概率下的多目标场景Experiment 3: Multi-target scenes with different detection probabilities

图7是不同检测概率环境下采用本发明MCST-GM-PHD与GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法的平均OSPA距离对比效果图。可以看出，在不同检测概率环境下本发明MCST-GM-PHD的目标状态估计精度优于GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法。Fig. 7 is a comparison effect diagram of the average OSPA distance using MCST-GM-PHD of the present invention and GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods under different detection probability environments. It can be seen that the target state estimation accuracy of MCST-GM-PHD of the present invention is better than that of GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods under different detection probability environments.

图8是不同检测概率环境下采用本发明MCST-GM-PHD与GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法的平均目标数目估计数对比效果图。可以看出，在不同检测概率环境下本发明MCST-GM-PHD的目标数目估计精度优于GM-PHD、P-GM-PHD、CP-GM-PHD和IR-GM-PHD方法。Fig. 8 is a comparison effect diagram of the average target number estimates using MCST-GM-PHD of the present invention and GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods under different detection probability environments. It can be seen that the target number estimation accuracy of MCST-GM-PHD of the present invention is better than that of GM-PHD, P-GM-PHD, CP-GM-PHD and IR-GM-PHD methods under different detection probability environments.

以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of the present invention. within the scope of protection.

Claims (6)

1.一种基于高斯混合概率假设密度的紧邻多目标跟踪方法，其特征在于，包括如下步骤：1. a kind of close neighbor multi-target tracking method based on Gaussian mixture probability hypothesis density, is characterized in that, comprises the steps: S1，增加高斯分量的标签和历史状态矩阵为辅助参数以构建用于表示目标的高斯分量的新标准描述集；S1, adding the label of the Gaussian component and the historical state matrix as auxiliary parameters to construct a new standard description set for the Gaussian component representing the target; 在步骤S1中，所述表示目标的高斯分量的新标准描述集的表达式为：In step S1, the expression of the new standard description set representing the Gaussian component of the target is:
Figure FDA00040368578400000118
Figure FDA00040368578400000118
 式中，w表示高斯分量的权值，m表示高斯分量的均值，P表示高斯分量的协方差矩阵，
Figure FDA00040368578400000119
表示高斯分量的标签，χ表示高斯分量的历史状态矩阵；In the formula, w represents the weight of the Gaussian component, m represents the mean value of the Gaussian component, P represents the covariance matrix of the Gaussian component,
Figure FDA00040368578400000119
Represents the label of the Gaussian component, and χ represents the historical state matrix of the Gaussian component; k时刻高斯分量的历史状态矩阵χk的表达式为：The expression of the historical state matrix χ k of the Gaussian component at time k is: χk＝[mk-δ+1,...,mk-1,mk]；χ k ＝[m k-δ+1 ,...,m k-1 ,m k ]; 式中，δ表示传感器所设定的历史状态矩阵中的元素数目阈值；In the formula, δ represents the threshold value of the number of elements in the historical state matrix set by the sensor; S2，初始化目标概率假设密度、目标标签集及目标历史状态矩阵集；S2, initialize the target probability hypothesis density, the target label set and the target historical state matrix set; 在步骤S2中，所述目标概率假设密度
Figure FDA0004036857840000011
的表达式为：In step S2, the target probability hypothesis density
Figure FDA0004036857840000011
The expression is:
Figure FDA0004036857840000012
Figure FDA0004036857840000012
 式中，
Figure FDA0004036857840000013
表示均值为m，协方差为P的高斯密度，x表示高斯分量o的状态，
Figure FDA0004036857840000014
表示k时刻第i个高斯分量
Figure FDA0004036857840000015
的权值，
Figure FDA0004036857840000016
表示k时刻第i个高斯分量
Figure FDA0004036857840000017
的均值，
Figure FDA0004036857840000018
表示k时刻第i个高斯分量
Figure FDA0004036857840000019
的协方差矩阵，Jk表示k时刻高斯分量的数目；In the formula,
Figure FDA0004036857840000013
Represents the Gaussian density with mean m and covariance P, x represents the state of Gaussian component o,
Figure FDA0004036857840000014
Indicates the i-th Gaussian component at time k
Figure FDA0004036857840000015
the weight of
Figure FDA0004036857840000016
Indicates the i-th Gaussian component at time k
Figure FDA0004036857840000017
the mean value of
Figure FDA0004036857840000018
Indicates the i-th Gaussian component at time k
Figure FDA0004036857840000019
The covariance matrix of , J k represents the number of Gaussian components at time k; 所述目标标签集
Figure FDA00040368578400000110
的表达式为：The target label set
Figure FDA00040368578400000110
The expression is:
Figure FDA00040368578400000111
Figure FDA00040368578400000111
 式中，
Figure FDA00040368578400000112
表示k时刻第i个高斯分量
Figure FDA00040368578400000113
的标签；In the formula,
Figure FDA00040368578400000112
Indicates the i-th Gaussian component at time k
Figure FDA00040368578400000113
Tag of; 所述目标历史状态矩阵集Λk的表达式为：The expression of the target historical state matrix set Λ k is:
Figure FDA00040368578400000114
Figure FDA00040368578400000114
 式中，
Figure FDA00040368578400000115
表示k时刻第i个高斯分量
Figure FDA00040368578400000116
的历史状态矩阵，且
Figure FDA00040368578400000117
In the formula,
Figure FDA00040368578400000115
Indicates the i-th Gaussian component at time k
Figure FDA00040368578400000116
The historical state matrix of , and
Figure FDA00040368578400000117
 S3，根据新生目标的概率假设密度、标签集、历史状态矩阵集和存活目标的预测概率假设密度、预测标签集、预测历史状态矩阵集，计算目标预测概率假设密度、目标预测标签集、目标预测历史状态矩阵集；S3, according to the probability hypothesis density, label set, historical state matrix set of the newborn target, and the predicted probability hypothesis density, predicted label set, and predicted historical state matrix set of the surviving target, calculate the target prediction probability hypothesis density, target prediction label set, and target prediction Historical state matrix set; 在步骤S3中，所述新生目标的概率假设密度γk(x)的表达式为：In step S3, the expression of the probability hypothesis density γ k (x) of the newborn target is:
Figure FDA0004036857840000021
Figure FDA0004036857840000021
 式中，Jγ,k表示新生高斯分量的数目，
Figure FDA0004036857840000022
表示k时刻第j个新生高斯分量
Figure FDA0004036857840000023
的权值，
Figure FDA0004036857840000024
表示k时刻第j个新生高斯分量
Figure FDA0004036857840000025
的均值，
Figure FDA0004036857840000026
表示k时刻第j个新生高斯分量
Figure FDA0004036857840000027
的协方差矩阵；In the formula, J γ,k represents the number of newborn Gaussian components,
Figure FDA0004036857840000022
Indicates the jth newborn Gaussian component at time k
Figure FDA0004036857840000023
the weight of
Figure FDA0004036857840000024
Indicates the jth newborn Gaussian component at time k
Figure FDA0004036857840000025
the mean value of
Figure FDA0004036857840000026
Indicates the jth newborn Gaussian component at time k
Figure FDA0004036857840000027
The covariance matrix of ; 所述新生目标的标签集
Figure FDA0004036857840000028
的表达式为：The tag set for the nascent target
Figure FDA0004036857840000028
The expression is:
Figure FDA0004036857840000029
Figure FDA0004036857840000029
 式中
Figure FDA00040368578400000210
表示第j个新生高斯分量
Figure FDA00040368578400000211
的标签；In the formula
Figure FDA00040368578400000210
Indicates the jth nascent Gaussian component
Figure FDA00040368578400000211
Tag of; 所述新生目标的历史状态矩阵集Λγ,k的表达式为：The historical state matrix set Λ γ of the newborn target, the expression of k is:
Figure FDA00040368578400000212
Figure FDA00040368578400000212
 式中，
Figure FDA00040368578400000213
表示第j个新生高斯分量
Figure FDA00040368578400000214
的历史状态矩阵，且
Figure FDA00040368578400000215
In the formula,
Figure FDA00040368578400000213
Indicates the jth nascent Gaussian component
Figure FDA00040368578400000214
The historical state matrix of , and
Figure FDA00040368578400000215
 所述存活目标的预测概率假设密度
Figure FDA00040368578400000216
的表达式为：The predicted probability hypothesis density for the survival target
Figure FDA00040368578400000216
The expression is:
Figure FDA00040368578400000217
Figure FDA00040368578400000217
 式中，
Figure FDA00040368578400000218
表示k时刻第i个存活高斯分量
Figure FDA00040368578400000219
的预测权值，
Figure FDA00040368578400000220
表示k时刻第i个存活高斯分量
Figure FDA00040368578400000221
的预测均值，
Figure FDA00040368578400000222
表示k时刻第i个存活高斯分量
Figure FDA00040368578400000223
的预测协方差矩阵，Js,k|k-1表示在k时刻用k-1时刻高斯分量数目Jk-1所预测的存活高斯分量的预测数目；In the formula,
Figure FDA00040368578400000218
Indicates the i-th surviving Gaussian component at time k
Figure FDA00040368578400000219
the predictive weight of
Figure FDA00040368578400000220
Indicates the i-th surviving Gaussian component at time k
Figure FDA00040368578400000221
the predicted mean of
Figure FDA00040368578400000222
Indicates the i-th surviving Gaussian component at time k
Figure FDA00040368578400000223
The prediction covariance matrix of , J s,k|k-1 represents the predicted number of surviving Gaussian components predicted by the number of Gaussian components J k - 1 at time k-1 at time k; 所述存活目标的预测标签集
Figure FDA00040368578400000224
的表达式为：The predicted label set of the surviving target
Figure FDA00040368578400000224
The expression is:
Figure FDA00040368578400000225
Figure FDA00040368578400000225
 式中，
Figure FDA00040368578400000226
表示k时刻第i个存活高斯分量
Figure FDA00040368578400000227
的预测标签，
Figure FDA00040368578400000228
表示k-1时刻第i个高斯分量
Figure FDA00040368578400000229
的标签；In the formula,
Figure FDA00040368578400000226
Indicates the i-th surviving Gaussian component at time k
Figure FDA00040368578400000227
the predicted label of
Figure FDA00040368578400000228
Represents the i-th Gaussian component at time k-1
Figure FDA00040368578400000229
Tag of; 所述存活目标的预测历史状态矩阵集Λs,k|k-1的表达式为：The expression of the predicted historical state matrix set Λ s,k|k-1 of the surviving target is:
Figure FDA00040368578400000230
Figure FDA00040368578400000230
 式中，
Figure FDA00040368578400000231
表示k时刻第i个存活高斯分量
Figure FDA00040368578400000232
的预测历史状态矩阵；
Figure FDA00040368578400000233
Figure FDA00040368578400000234
表示k-1时刻第i个高斯分量
Figure FDA00040368578400000235
的历史状态矩阵
Figure FDA00040368578400000236
的第2列向量，
Figure FDA00040368578400000237
表示k-1时刻第i个高斯分量
Figure FDA00040368578400000238
的历史状态矩阵
Figure FDA00040368578400000239
的第δ列向量；In the formula,
Figure FDA00040368578400000231
Indicates the i-th surviving Gaussian component at time k
Figure FDA00040368578400000232
The predicted historical state matrix of ;
Figure FDA00040368578400000233
Figure FDA00040368578400000234
Represents the i-th Gaussian component at time k-1
Figure FDA00040368578400000235
The historical state matrix of
Figure FDA00040368578400000236
The 2nd column vector of ,
Figure FDA00040368578400000237
Represents the i-th Gaussian component at time k-1
Figure FDA00040368578400000238
The historical state matrix of
Figure FDA00040368578400000239
The δth column vector of ; 所述目标预测概率假设密度
Figure FDA0004036857840000031
的表达式为：The target predicted probability hypothesis density
Figure FDA0004036857840000031
The expression is:
Figure FDA0004036857840000032
Figure FDA0004036857840000032
 式中，Jk|k-1表示预测高斯分量的预测数目，
Figure FDA0004036857840000033
表示第i个预测高斯分量
Figure FDA0004036857840000034
的预测权值，
Figure FDA0004036857840000035
表示第i个预测高斯分量
Figure FDA0004036857840000036
的预测均值，
Figure FDA0004036857840000037
表示第i个预测高斯分量
Figure FDA0004036857840000038
的预测协方差矩阵；In the formula, J k|k-1 represents the predicted number of predicted Gaussian components,
Figure FDA0004036857840000033
Indicates the i-th predicted Gaussian component
Figure FDA0004036857840000034
the predictive weight of
Figure FDA0004036857840000035
Indicates the i-th predicted Gaussian component
Figure FDA0004036857840000036
the predicted mean of
Figure FDA0004036857840000037
Indicates the i-th predicted Gaussian component
Figure FDA0004036857840000038
The prediction covariance matrix of ; 所述目标预测标签集
Figure FDA0004036857840000039
的表达式为：The target prediction label set
Figure FDA0004036857840000039
The expression is:
Figure FDA00040368578400000310
Figure FDA00040368578400000310
 式中，
Figure FDA00040368578400000311
表示第i个预测高斯分量
Figure FDA00040368578400000312
的预测标签；In the formula,
Figure FDA00040368578400000311
Indicates the i-th predicted Gaussian component
Figure FDA00040368578400000312
the predicted label; 所述目标预测历史状态矩阵集Λk|k-1的表达式为：The expression of the target prediction historical state matrix set Λ k|k-1 is:
Figure FDA00040368578400000313
Figure FDA00040368578400000313
 式中，
Figure FDA00040368578400000314
表示第i个预测高斯分量
Figure FDA00040368578400000315
的预测历史状态矩阵；In the formula,
Figure FDA00040368578400000314
Indicates the i-th predicted Gaussian component
Figure FDA00040368578400000315
The predicted historical state matrix of ; S4，基于量测集计算目标后验概率假设密度、目标后验标签集和目标后验历史状态矩阵集，重分配目标后验概率假设密度中各高斯分量的权值；S4. Calculate the target posterior probability hypothesis density, the target posterior label set and the target posterior historical state matrix set based on the measurement set, and redistribute the weights of each Gaussian component in the target posterior probability hypothesis density; S5，对目标的高斯分量集及其参数集进行变换，并对变换后的高斯分量集进行约简；S5, transforming the target Gaussian component set and its parameter set, and reducing the transformed Gaussian component set; S6，估计目标的状态和数目；S6, estimating the state and number of targets; 在步骤S6中，所述估计目标的状态和数目包括如下步骤：In step S6, said estimating the state and number of targets includes the following steps: S6.1，根据步骤S5中所获得的高斯分量参数集中的权值估计目标数目；S6.1, estimating the number of targets according to the weights in the Gaussian component parameter set obtained in step S5; 所述目标数目Nk的表达式为：The expression of the target number N k is:
Figure FDA00040368578400000316
Figure FDA00040368578400000316
 式中，
Figure FDA00040368578400000317
表示高斯分量
Figure FDA00040368578400000318
的权值，Jk表示k时刻高斯分量的数目；In the formula,
Figure FDA00040368578400000317
Represents the Gaussian component
Figure FDA00040368578400000318
The weight of , J k represents the number of Gaussian components at time k; S6.2，从高斯分量参数集中选择权值大于0.5的索引，之后将索引所对应的高斯分量作为真实目标，最后输出高斯分量的均值即作为当前时刻的目标状态估计；S6.2, select an index with a weight greater than 0.5 from the Gaussian component parameter set, then use the Gaussian component corresponding to the index as the real target, and finally output the mean value of the Gaussian component as the target state estimate at the current moment; S7，若跟踪单一时刻，则目标跟踪结束；若跟踪若干个时刻，则重复执行S3-S6直至迭代所有时刻。S7. If a single moment is tracked, the target tracking ends; if several moments are tracked, S3-S6 is repeatedly executed until all moments are iterated. 2.根据权利要求1所述的基于高斯混合概率假设密度的紧邻多目标跟踪方法，其特征在于，在步骤S4中，所述量测集Zk的表达式为：2. the close neighbor multi-target tracking method based on Gaussian mixture probability hypothesis density according to claim 1, is characterized in that, in step S4, the expression of described measuring set Z k is:
Figure FDA0004036857840000041
Figure FDA0004036857840000041
 式中，Mk表示k时刻量测集Zk中量测的数目，
Figure FDA0004036857840000042
表示量测集Zk中的第j个量测；In the formula, M k represents the number of measurements in the measurement set Z k at time k,
Figure FDA0004036857840000042
Indicates the jth measurement in the measurement set Z k ; 所述计算目标后验概率假设密度
Figure FDA0004036857840000043
目标后验标签集
Figure FDA0004036857840000044
和目标后验历史状态矩阵集Λk，包括如下步骤：The computed target posterior probability hypothesis density
Figure FDA0004036857840000043
target posterior label set
Figure FDA0004036857840000044
and the target posterior historical state matrix set Λ k , including the following steps: S4.1；计算高斯分量
Figure FDA0004036857840000045
的权值
Figure FDA0004036857840000046
均值
Figure FDA0004036857840000047
协方差矩阵
Figure FDA0004036857840000048
标签
Figure FDA0004036857840000049
历史状态矩阵
Figure FDA00040368578400000410
S4.1; Calculation of Gaussian components
Figure FDA0004036857840000045
weight of
Figure FDA0004036857840000046
average
Figure FDA0004036857840000047
covariance matrix
Figure FDA0004036857840000048
Label
Figure FDA0004036857840000049
Historical State Matrix
Figure FDA00040368578400000410
 所述高斯分量
Figure FDA00040368578400000411
的权值
Figure FDA00040368578400000412
的表达式为：The Gaussian component
Figure FDA00040368578400000411
weight of
Figure FDA00040368578400000412
The expression is:
Figure FDA00040368578400000413
Figure FDA00040368578400000413
 式中，
Figure FDA00040368578400000414
表示基于量测
Figure FDA00040368578400000415
的杂波强度，pd表示检测概率，Hk表示k时刻量测矩阵；Rk表示k时刻量测噪声协方差矩阵，
Figure FDA00040368578400000416
表示预测高斯分量
Figure FDA00040368578400000417
的预测权值，
Figure FDA00040368578400000418
表示预测高斯分量
Figure FDA00040368578400000419
的预测均值，
Figure FDA00040368578400000420
表示预测高斯分量
Figure FDA00040368578400000421
的预测协方差矩阵；In the formula,
Figure FDA00040368578400000414
Indicates based on measurement
Figure FDA00040368578400000415
clutter intensity, p d represents the detection probability, H k represents the measurement matrix at time k; R k represents the measurement noise covariance matrix at time k,
Figure FDA00040368578400000416
represents the predicted Gaussian component
Figure FDA00040368578400000417
the predictive weight of
Figure FDA00040368578400000418
represents the predicted Gaussian component
Figure FDA00040368578400000419
the predicted mean of
Figure FDA00040368578400000420
represents the predicted Gaussian component
Figure FDA00040368578400000421
The prediction covariance matrix of ; 所述高斯分量
Figure FDA00040368578400000422
的均值
Figure FDA00040368578400000423
的表达式为：The Gaussian component
Figure FDA00040368578400000422
mean of
Figure FDA00040368578400000423
The expression is:
Figure FDA00040368578400000424
Figure FDA00040368578400000424
 式中，
Figure FDA00040368578400000425
表示高斯分量
Figure FDA00040368578400000426
的信息增益，且
Figure FDA00040368578400000427
In the formula,
Figure FDA00040368578400000425
Represents the Gaussian component
Figure FDA00040368578400000426
information gain, and
Figure FDA00040368578400000427
 所述高斯分量
Figure FDA00040368578400000428
的协方差矩阵
Figure FDA00040368578400000429
的表达式为：The Gaussian component
Figure FDA00040368578400000428
The covariance matrix of
Figure FDA00040368578400000429
The expression is:
Figure FDA00040368578400000430
Figure FDA00040368578400000430
 式中，I表示单位矩阵；In the formula, I represents the identity matrix; 所述高斯分量
Figure FDA00040368578400000431
的标签
Figure FDA00040368578400000432
的表达式为：The Gaussian component
Figure FDA00040368578400000431
Tag of
Figure FDA00040368578400000432
The expression is:
Figure FDA00040368578400000433
Figure FDA00040368578400000433
 所述高斯分量
Figure FDA00040368578400000434
的历史状态矩阵
Figure FDA00040368578400000435
的表达式为：The Gaussian component
Figure FDA00040368578400000434
The historical state matrix of
Figure FDA00040368578400000435
The expression is:
Figure FDA00040368578400000436
Figure FDA00040368578400000436
 式中，
Figure FDA00040368578400000437
表示预测高斯分量
Figure FDA00040368578400000438
的预测历史状态矩阵
Figure FDA00040368578400000439
的第1列向量，
Figure FDA00040368578400000440
表示预测高斯分量
Figure FDA00040368578400000441
的预测历史状态矩阵
Figure FDA00040368578400000442
的第δ-1列向量，
Figure FDA00040368578400000443
表示高斯分量
Figure FDA00040368578400000444
的均值；In the formula,
Figure FDA00040368578400000437
represents the predicted Gaussian component
Figure FDA00040368578400000438
The forecast history state matrix of
Figure FDA00040368578400000439
The first column vector of ,
Figure FDA00040368578400000440
represents the predicted Gaussian component
Figure FDA00040368578400000441
The forecast history state matrix of
Figure FDA00040368578400000442
The δ-1th column vector of ,
Figure FDA00040368578400000443
Represents the Gaussian component
Figure FDA00040368578400000444
the mean value of S4.2，计算高斯分量
Figure FDA0004036857840000051
所对应的非归一化权值矩阵Ak和归一化权值矩阵Bk，以对各高斯分量的权值进行再分配，输出目标后验概率假设密度
Figure FDA0004036857840000052
目标后验标签集
Figure FDA0004036857840000053
和目标后验历史状态矩阵集Λk；S4.2, Calculation of Gaussian components
Figure FDA0004036857840000051
The corresponding unnormalized weight matrix A k and normalized weight matrix B k are used to redistribute the weights of each Gaussian component, and output the target posterior probability hypothesis density
Figure FDA0004036857840000052
target posterior label set
Figure FDA0004036857840000053
and the target posterior history state matrix set Λ k ; 所述非归一化权值矩阵Ak的表达式为：The expression of the non-normalized weight matrix A k is:
Figure FDA0004036857840000054
Figure FDA0004036857840000054
 式中，
Figure FDA0004036857840000055
表示高斯分量
Figure FDA0004036857840000056
的非归一化权值，且
Figure FDA0004036857840000057
In the formula,
Figure FDA0004036857840000055
Represents the Gaussian component
Figure FDA0004036857840000056
The unnormalized weights of , and
Figure FDA0004036857840000057
 归一化权值矩阵Bk的表达式为：The expression of the normalized weight matrix B k is:
Figure FDA0004036857840000058
Figure FDA0004036857840000058
 式中，
Figure FDA0004036857840000059
表示高斯分量
Figure FDA00040368578400000510
的权值。In the formula,
Figure FDA0004036857840000059
Represents the Gaussian component
Figure FDA00040368578400000510
weights. 3.根据权利要求2所述的基于高斯混合概率假设密度的紧邻多目标跟踪方法，其特征在于，在步骤S4.2中，所述对各高斯分量的权值进行再分配，输出目标后验概率假设密度
Figure FDA00040368578400000511
目标后验标签集
Figure FDA00040368578400000512
和目标后验历史状态矩阵集Λk包括如下步骤：3. The adjacent multiple target tracking method based on Gaussian mixture probability hypothesis density according to claim 2, characterized in that, in step S4.2, the weights of each Gaussian component are redistributed, and the output target posterior probability hypothesis density
Figure FDA00040368578400000511
target posterior label set
Figure FDA00040368578400000512
and the target posterior historical state matrix set Λ k include the following steps: S4.2.1，查找归一化权值矩阵Bk中的最大权值的索引<i*,j*>，构建与该最大权值高斯分量具有相同标签的高斯分量的分量索引集Ψ，计算分量索引集Ψ中索引所对应的高斯分量的权值和ηw；S4.2.1, find the index <i * , j * > of the maximum weight in the normalized weight matrix B k , construct the component index set Ψ of the Gaussian component with the same label as the maximum weight Gaussian component, and calculate the component The weight sum η w of the Gaussian component corresponding to the index in the index set Ψ; 所述最大权值的索引<i*,j*>的表达式为：The expression of the index <i * , j * > of the maximum weight is:
Figure FDA00040368578400000513
Figure FDA00040368578400000513
 式中，
Figure FDA00040368578400000514
为高斯分量索引集，且其初始值为
Figure FDA00040368578400000515
Mk表示k时刻量测集Zk中量测的数目；In the formula,
Figure FDA00040368578400000514
is the Gaussian component index set, and its initial value is
Figure FDA00040368578400000515
M k represents the number of measurements in the measurement set Z k at time k; 所述分量索引集Ψ的表达式为：The expression of the component index set Ψ is:
Figure FDA00040368578400000516
Figure FDA00040368578400000516
 式中，
Figure FDA00040368578400000517
表示高斯分量
Figure FDA00040368578400000518
的标签，
Figure FDA00040368578400000519
表示高斯分量
Figure FDA00040368578400000520
的标签；In the formula,
Figure FDA00040368578400000517
Represents the Gaussian component
Figure FDA00040368578400000518
Tag of,
Figure FDA00040368578400000519
Represents the Gaussian component
Figure FDA00040368578400000520
Tag of; 所述权值和ηw的表达式为：The expression of described weight and η w is:
Figure FDA0004036857840000061
Figure FDA0004036857840000061
 S4.2.2，计算标志位
Figure FDA0004036857840000062
如果标志位
Figure FDA0004036857840000063
则更新分量索引集Ψ中索引所对应的高斯分量的权值和ηw和标志位
Figure FDA0004036857840000064
若标志位
Figure FDA0004036857840000065
则执行步骤S4.2.3；S4.2.2, Calculation flag bit
Figure FDA0004036857840000062
if flag
Figure FDA0004036857840000063
Then update the weight and η w and the flag bit of the Gaussian component corresponding to the index in the component index set Ψ
Figure FDA0004036857840000064
if flag
Figure FDA0004036857840000065
Then execute step S4.2.3; 所述标志位
Figure FDA0004036857840000066
的表达式为：The flag bit
Figure FDA0004036857840000066
The expression is:
Figure FDA0004036857840000067
Figure FDA0004036857840000067
 S4.2.3，将归一化权值矩阵Bk中的权值
Figure FDA0004036857840000068
拷贝到优化权值矩阵Ek中的对应位置，其中，i∈Ψ、j＝1:Mk；S4.2.3, normalize the weights in the weight matrix B k
Figure FDA0004036857840000068
Copy to the corresponding position in the optimization weight matrix E k , wherein, i∈Ψ, j=1:M k ; S4.2.4，更新高斯分量索引集
Figure FDA0004036857840000069
如果高斯分量索引集
Figure FDA00040368578400000610
为空，则继续执行步骤S4.2.5，否则返回执行步骤S4.2.1；S4.2.4, update Gaussian component index set
Figure FDA0004036857840000069
If the Gaussian component index set
Figure FDA00040368578400000610
If it is empty, continue to execute step S4.2.5, otherwise return to execute step S4.2.1; S4.2.5，基于优化权值矩阵Ek中的权值，更新目标后验概率假设密度
Figure FDA00040368578400000611
中的相应高斯分量的权值；输出目标后验概率假设密度
Figure FDA00040368578400000612
目标后验标签集
Figure FDA00040368578400000613
和目标后验历史状态矩阵集Λk；S4.2.5, update the target posterior probability hypothesis density based on the weights in the optimized weight matrix E k
Figure FDA00040368578400000611
The weights of the corresponding Gaussian components in ; the output target posterior probability hypothesis density
Figure FDA00040368578400000612
target posterior label set
Figure FDA00040368578400000613
and the target posterior history state matrix set Λ k ; 所述目标后验概率假设密度
Figure FDA00040368578400000614
的表达式为：The target posterior probability hypothesis density
Figure FDA00040368578400000614
The expression is:
Figure FDA00040368578400000615
Figure FDA00040368578400000615
 所述目标后验标签集
Figure FDA00040368578400000616
的表达式为：The target posterior label set
Figure FDA00040368578400000616
The expression is:
Figure FDA00040368578400000617
Figure FDA00040368578400000617
 所述目标后验历史状态矩阵集Λk的表达式为：The expression of the target posterior history state matrix set Λ k is:
Figure FDA00040368578400000618
Figure FDA00040368578400000618
 4.根据权利要求3所述的基于高斯混合概率假设密度的紧邻多目标跟踪方法，其特征在于，在步骤S4.2.2中，所述更新分量索引集中索引所对应的高斯分量的权值和ηw和标志位
Figure FDA00040368578400000619
包括如下步骤：4. the close neighbor multi-target tracking method based on Gaussian mixture probability hypothesis density according to claim 3, is characterized in that, in step S4.2.2, the weight sum η of the Gaussian component corresponding to the index set index set of the update component w and flags
Figure FDA00040368578400000619
Including the following steps: S4.2.2a，从具有相同标签
Figure FDA00040368578400000620
的高斯分量中选择具有最小加权Hungarian距离的高斯分量；S4.2.2a, from the same label
Figure FDA00040368578400000620
Select the Gaussian component with the smallest weighted Hungarian distance among the Gaussian components of ; 所述高斯分量所对应的索引＜ir,jc＞的表达式为：The expression of the index <i r , j c > corresponding to the Gaussian component is:
Figure FDA00040368578400000621
Figure FDA00040368578400000621
 其中，
Figure FDA0004036857840000071
in,
Figure FDA0004036857840000071
 式中，比例系数ζ＝[1,δ-1/δ,δ-2/δ,δ-3/δ,δ-4/δ]，
Figure FDA0004036857840000072
表示高斯分量
Figure FDA0004036857840000073
在k时刻的历史状态矩阵
Figure FDA0004036857840000074
的第l列向量，
Figure FDA0004036857840000075
表示
Figure FDA0004036857840000076
与量测
Figure FDA0004036857840000077
间的Hungarian距离，其中，
Figure FDA0004036857840000078
In the formula, the proportional coefficient ζ=[1, δ-1/δ, δ-2/δ, δ-3/δ, δ-4/δ],
Figure FDA0004036857840000072
Represents the Gaussian component
Figure FDA0004036857840000073
Historical state matrix at time k
Figure FDA0004036857840000074
The l-th column of the vector,
Figure FDA0004036857840000075
express
Figure FDA0004036857840000076
and measurement
Figure FDA0004036857840000077
The Hungarian distance between, where,
Figure FDA0004036857840000078
 S4.2.2b，更新非归一化权值矩阵Ak和归一化权值矩阵Bk中的各权值，对应的表达式分别为：S4.2.2b, update the weights in the unnormalized weight matrix A k and the normalized weight matrix B k , the corresponding expressions are respectively:
Figure FDA0004036857840000079
Figure FDA0004036857840000079
 式中，比例因子
Figure FDA00040368578400000710
Figure FDA00040368578400000711
表示高斯分量
Figure FDA00040368578400000712
的标签；In the formula, the scale factor
Figure FDA00040368578400000710
Figure FDA00040368578400000711
Represents the Gaussian component
Figure FDA00040368578400000712
Tag of;
Figure FDA00040368578400000713
Figure FDA00040368578400000713
 S4.2.2c，更新分量索引集Ψ中索引所对应的高斯分量的权值和ηw和标志位
Figure FDA00040368578400000714
如果标志位
Figure FDA00040368578400000715
则返回执行步骤S4.2.2b，若标志位
Figure FDA00040368578400000716
则执行步骤S4.2.3。S4.2.2c, update the weight and η w and flag bit of the Gaussian component corresponding to the index in the component index set Ψ
Figure FDA00040368578400000714
if flag
Figure FDA00040368578400000715
Then return to step S4.2.2b, if the flag
Figure FDA00040368578400000716
Then execute step S4.2.3. 5.根据权利要求1或4所述的基于高斯混合概率假设密度的紧邻多目标跟踪方法，其特征在于，在步骤S5中，所述目标的高斯分量集的表达式为：5. according to claim 1 or 4 described based on Gaussian mixture probability hypothesis density close neighbor multi-target tracking method, it is characterized in that, in step S5, the expression of the Gaussian component set of described target is:
Figure FDA00040368578400000717
Figure FDA00040368578400000717
 式中，Jk|k-1表示预测高斯分量的预测数目，Mk表示量测集Zk中量测的数目；In the formula, J k|k-1 represents the predicted number of predicted Gaussian components, and M k represents the number of measurements in the measurement set Z k ; 所述参数集的表达式为：The expression of the parameter set is:
Figure FDA00040368578400000718
Figure FDA00040368578400000718
 式中，
Figure FDA00040368578400000719
表示预测高斯分量
Figure FDA00040368578400000720
的预测权值，
Figure FDA00040368578400000721
表示预测高斯分量
Figure FDA00040368578400000722
的预测均值，
Figure FDA00040368578400000723
表示预测高斯分量
Figure FDA00040368578400000724
的预测协方差矩阵，
Figure FDA00040368578400000725
表示预测高斯分量
Figure FDA00040368578400000726
的预测标签，
Figure FDA00040368578400000727
表示预测高斯分量
Figure FDA00040368578400000728
的预测历史状态矩阵，
Figure FDA00040368578400000729
表示高斯分量
Figure FDA00040368578400000730
的权值，
Figure FDA00040368578400000731
表示高斯分量
Figure FDA00040368578400000732
的均值，
Figure FDA00040368578400000733
表示高斯分量
Figure FDA00040368578400000734
的协方差矩阵，
Figure FDA00040368578400000735
表示高斯分量
Figure FDA00040368578400000736
的标签，
Figure FDA00040368578400000737
表示高斯分量
Figure FDA00040368578400000738
的历史状态矩阵；In the formula,
Figure FDA00040368578400000719
represents the predicted Gaussian component
Figure FDA00040368578400000720
the predictive weight of
Figure FDA00040368578400000721
represents the predicted Gaussian component
Figure FDA00040368578400000722
the predicted mean of
Figure FDA00040368578400000723
represents the predicted Gaussian component
Figure FDA00040368578400000724
The prediction covariance matrix of ,
Figure FDA00040368578400000725
represents the predicted Gaussian component
Figure FDA00040368578400000726
the predicted label of
Figure FDA00040368578400000727
represents the predicted Gaussian component
Figure FDA00040368578400000728
The predicted history state matrix of ,
Figure FDA00040368578400000729
Represents the Gaussian component
Figure FDA00040368578400000730
the weight of
Figure FDA00040368578400000731
Represents the Gaussian component
Figure FDA00040368578400000732
the mean value of
Figure FDA00040368578400000733
Represents the Gaussian component
Figure FDA00040368578400000734
The covariance matrix of ,
Figure FDA00040368578400000735
Represents the Gaussian component
Figure FDA00040368578400000736
Tag of,
Figure FDA00040368578400000737
Represents the Gaussian component
Figure FDA00040368578400000738
The historical state matrix of ; 所述变换后的高斯分量集的表达式为：The expression of the transformed Gaussian component set is:
Figure FDA00040368578400000739
Figure FDA00040368578400000739
 式中，高斯分量数目Jk为Jk＝Jk|k-1+Jk|k-1×Mk；In the formula, the number of Gaussian components J k is J k ＝J k|k-1 +J k|k-1 ×M k ; 所述变换后的高斯分量集所对应的参数集表达式为：The parameter set expression corresponding to the transformed Gaussian component set is:
Figure FDA0004036857840000081
Figure FDA0004036857840000081
 所述对变换后的高斯分量集进行约简包括步骤如下：The step of reducing the transformed Gaussian component set includes the following steps: S5.1，设定删减阈值T1，融合阈值U，最大高斯分量数目阈值Jmax；S5.1, set the pruning threshold T 1 , the fusion threshold U, the maximum Gaussian component number threshold J max ; S5.2，设定计数变量j＝0和高斯分量数目变量
Figure FDA0004036857840000082
高斯分量索引集
Figure FDA0004036857840000083
S5.2, set count variable j=0 and Gaussian component number variable
Figure FDA0004036857840000082
Gaussian component index set
Figure FDA0004036857840000083
 式中，
Figure FDA0004036857840000084
表示高斯分量
Figure FDA0004036857840000085
的权值；In the formula,
Figure FDA0004036857840000084
Represents the Gaussian component
Figure FDA0004036857840000085
the weight of S5.3，执行j＝j+1，筛选具有最大权值的高斯分量
Figure FDA0004036857840000086
以建立新的高斯分量；S5.3, execute j=j+1, and filter the Gaussian component with the largest weight
Figure FDA0004036857840000086
to create a new Gaussian component; 所述最大权值的高斯分量
Figure FDA0004036857840000087
的索引l*的表达式为：the Gaussian component of the maximum weight
Figure FDA0004036857840000087
The expression for the index l * is:
Figure FDA0004036857840000088
Figure FDA0004036857840000088
 S5.4，更新高斯分量索引集
Figure FDA0004036857840000089
若高斯分量索引集
Figure FDA00040368578400000810
不为空，则返回执行步骤S5.3；若高斯分量索引集
Figure FDA00040368578400000811
为空，更新高斯分量数目变量
Figure FDA00040368578400000812
且执行步骤S5.5；S5.4, update Gaussian component index set
Figure FDA0004036857840000089
If the Gaussian component index set
Figure FDA00040368578400000810
is not empty, return to step S5.3; if Gaussian component index set
Figure FDA00040368578400000811
If it is empty, update the Gaussian component number variable
Figure FDA00040368578400000812
And execute step S5.5; 所述更新高斯分量索引集
Figure FDA00040368578400000813
的表达式为：The updated Gaussian component index set
Figure FDA00040368578400000813
The expression is:
Figure FDA00040368578400000814
Figure FDA00040368578400000814
 式中，过渡索引集
Figure FDA00040368578400000815
Figure FDA00040368578400000816
表示最大权值的高斯分量
Figure FDA00040368578400000817
的标签，
Figure FDA00040368578400000818
表示高斯分量
Figure FDA00040368578400000819
的标签；In the formula, the transition index set
Figure FDA00040368578400000815
Figure FDA00040368578400000816
Gaussian component representing the maximum weight
Figure FDA00040368578400000817
Tag of,
Figure FDA00040368578400000818
Represents the Gaussian component
Figure FDA00040368578400000819
Tag of; 所述更新高斯分量数目变量
Figure FDA00040368578400000820
的表达式为：The updated Gaussian component number variable
Figure FDA00040368578400000820
The expression is:
Figure FDA00040368578400000821
Figure FDA00040368578400000821
 S5.5，对高斯分量数目变量
Figure FDA00040368578400000822
和最大高斯分量数目阈值Jmax的值进行比较，根据新的高斯分量集
Figure FDA00040368578400000823
获得约简后的高斯分量集
Figure FDA00040368578400000824
S5.5, for the number of Gaussian components variable
Figure FDA00040368578400000822
Compared with the value of the maximum Gaussian component number threshold J max , according to the new Gaussian component set
Figure FDA00040368578400000823
Obtain the reduced Gaussian component set
Figure FDA00040368578400000824
 如果
Figure FDA00040368578400000825
按权值
Figure FDA00040368578400000826
由大到小的顺序对所获得的新的高斯分量集
Figure FDA00040368578400000827
进行排列，取前Jmax个高斯分量构建约简后的高斯分量集
Figure FDA00040368578400000828
其中
Figure FDA00040368578400000829
Jk＝Jmax；若
Figure FDA00040368578400000830
则新的高斯分量集
Figure FDA00040368578400000831
为约简后的高斯分量集
Figure FDA00040368578400000832
其中
Figure FDA00040368578400000833
if
Figure FDA00040368578400000825
by weight
Figure FDA00040368578400000826
The new set of Gaussian components obtained by ordering from large to small
Figure FDA00040368578400000827
Arrange and take the first J max Gaussian components to construct the reduced Gaussian component set
Figure FDA00040368578400000828
in
Figure FDA00040368578400000829
J k = J max ; if
Figure FDA00040368578400000830
Then the new set of Gaussian components
Figure FDA00040368578400000831
is the reduced Gaussian component set
Figure FDA00040368578400000832
in
Figure FDA00040368578400000833
 6.根据权利要求5所述的基于高斯混合概率假设密度的紧邻多目标跟踪方法，其特征在于，在步骤S5.3中，所述建立新的高斯分量包括如下步骤：6. The method for tracking multiple targets in close proximity based on Gaussian mixture probability hypothesis density according to claim 5, characterized in that, in step S5.3, said establishing a new Gaussian component comprises the following steps: S5.3.1，定义过渡索引集
Figure FDA00040368578400000834
S5.3.1, Define Transition Index Sets
Figure FDA00040368578400000834
 式中，
Figure FDA00040368578400000835
表示最大权值的高斯分量
Figure FDA00040368578400000836
的标签；In the formula,
Figure FDA00040368578400000835
Gaussian component representing the maximum weight
Figure FDA00040368578400000836
Tag of; S5.3.2，定义过渡索引集
Figure FDA0004036857840000091
S5.3.2, Define Transition Index Sets
Figure FDA0004036857840000091
 式中，
Figure FDA0004036857840000092
表示最大权值的高斯分量
Figure FDA0004036857840000093
的均值，
Figure FDA0004036857840000094
表示最大权值的高斯分量
Figure FDA0004036857840000095
的协方差矩阵，
Figure FDA0004036857840000096
表示高斯分量
Figure FDA0004036857840000097
的均值；In the formula,
Figure FDA0004036857840000092
Gaussian component representing the maximum weight
Figure FDA0004036857840000093
the mean value of
Figure FDA0004036857840000094
Gaussian component representing the maximum weight
Figure FDA0004036857840000095
The covariance matrix of ,
Figure FDA0004036857840000096
Represents the Gaussian component
Figure FDA0004036857840000097
the mean value of S5.3.3，将过渡索引集L2中索引所对应的高斯分量
Figure FDA0004036857840000098
合并为一个新的高斯分量
Figure FDA0004036857840000099
S5.3.3, the Gaussian component corresponding to the index in the transition index set L2
Figure FDA0004036857840000098
combined into a new Gaussian component
Figure FDA0004036857840000099
 所述新的高斯分量
Figure FDA00040368578400000910
的权值
Figure FDA00040368578400000911
的表达式为：The new Gaussian component
Figure FDA00040368578400000910
weight of
Figure FDA00040368578400000911
The expression is:
Figure FDA00040368578400000912
Figure FDA00040368578400000912
 式中，
Figure FDA00040368578400000913
表示高斯分量
Figure FDA00040368578400000914
的权值；In the formula,
Figure FDA00040368578400000913
Represents the Gaussian component
Figure FDA00040368578400000914
the weight of 所述新的高斯分量
Figure FDA00040368578400000915
的均值
Figure FDA00040368578400000916
的表达式为：The new Gaussian component
Figure FDA00040368578400000915
mean of
Figure FDA00040368578400000916
The expression is:
Figure FDA00040368578400000917
Figure FDA00040368578400000917
 所述新的高斯分量
Figure FDA00040368578400000918
的协方差矩阵
Figure FDA00040368578400000919
的表达式为：The new Gaussian component
Figure FDA00040368578400000918
The covariance matrix of
Figure FDA00040368578400000919
The expression is:
Figure FDA00040368578400000920
Figure FDA00040368578400000920
 式中，
Figure FDA00040368578400000921
表示最大权值的高斯分量
Figure FDA00040368578400000922
的均值，
Figure FDA00040368578400000923
表示高斯分量
Figure FDA00040368578400000924
的协方差矩阵；In the formula,
Figure FDA00040368578400000921
Gaussian component representing the maximum weight
Figure FDA00040368578400000922
the mean value of
Figure FDA00040368578400000923
Represents the Gaussian component
Figure FDA00040368578400000924
The covariance matrix of ; 所述新的高斯分量
Figure FDA00040368578400000925
的标签
Figure FDA00040368578400000926
的表达式为：The new Gaussian component
Figure FDA00040368578400000925
Tag of
Figure FDA00040368578400000926
The expression is:
Figure FDA00040368578400000927
Figure FDA00040368578400000927
 所述新的高斯分量
Figure FDA00040368578400000928
的历史状态矩阵
Figure FDA00040368578400000929
的表达式为：The new Gaussian component
Figure FDA00040368578400000928
The historical state matrix of
Figure FDA00040368578400000929
The expression is:
Figure FDA00040368578400000930
Figure FDA00040368578400000930
 式中，
Figure FDA00040368578400000931
表示最大权值的高斯分量
Figure FDA00040368578400000932
的历史状态矩阵
Figure FDA00040368578400000933
的第1列向量，
Figure FDA00040368578400000934
表示最大权值的高斯分量
Figure FDA00040368578400000935
的历史状态矩阵
Figure FDA00040368578400000936
的第δ-1列向量。In the formula,
Figure FDA00040368578400000931
Gaussian component representing the maximum weight
Figure FDA00040368578400000932
The historical state matrix of
Figure FDA00040368578400000933
The first column vector of ,
Figure FDA00040368578400000934
Gaussian component representing the maximum weight
Figure FDA00040368578400000935
The historical state matrix of
Figure FDA00040368578400000936
The δ-1th column vector of .
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